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Three rational numbers x, y, z satisfy x + y + z = 0 and xy + yz + zx = 0. Show that all the rational numbers x, y, z must be simultaneously zero.
We are given two equations: x + y + z = 0 and xy + yz + zx = 0. Using the algebraic identity, we know that (x + y + z) squared equals x2 + y2 + z2 + 2(xy + yz + zx). Substituting our given values into this identity results in 0 squared equals x2 + y2 + z2 + 2(0), which simplifies directly to x2 + y2Read more
We are given two equations: x + y + z = 0 and xy + yz + zx = 0. Using the algebraic identity, we know that (x + y + z) squared equals x2 + y2 + z2 + 2(xy + yz + zx). Substituting our given values into this identity results in 0 squared equals x2 + y2 + z2 + 2(0), which simplifies directly to x2 + y2 + z2 = 0. Since the square of any real rational number is always non-negative, their sum can only equal zero if x, y, and z are all simultaneously zero.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessA rational number in its lowest form has denominator 2³ × 5. How many decimal places will its decimal expansion have? Explain your answer.
The denominator of the rational number in its lowest form is given as 2 cubed times 5, which equals 8 times 5, or 40. A fraction with a denominator of the form 2 raised to m times 5 raised to n will always have a terminating decimal expansion. The number of decimal places is determined by the higherRead more
The denominator of the rational number in its lowest form is given as 2 cubed times 5, which equals 8 times 5, or 40. A fraction with a denominator of the form 2 raised to m times 5 raised to n will always have a terminating decimal expansion. The number of decimal places is determined by the higher exponent of the prime factors 2 and 5. Since the exponent of 2 is 3, it will have exactly 3 decimal places.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessFind 5 rational numbers between1/6 and 2/5.
To find 5 rational numbers between 1/6 and 2/5, we first convert them to have a common denominator. The least common multiple of 6 and 5 is 30, making the fractions 5/30 and 12/30. Since there is a sufficient gap between the numerators 5 and 12, we can directly choose five intermediate values. Thus,Read more
To find 5 rational numbers between 1/6 and 2/5, we first convert them to have a common denominator. The least common multiple of 6 and 5 is 30, making the fractions 5/30 and 12/30. Since there is a sufficient gap between the numerators 5 and 12, we can directly choose five intermediate values. Thus, the five rational numbers are 6/30, 7/30, 8/30, 9/30, and 10/30.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessFind 5 rational numbers between 2/5 and 3/5 .
To find 5 rational numbers between 2/5 and 3/5, we can scale up the fractions to have a larger common denominator. Multiplying the numerator and denominator of both fractions by 6 transforms them into 12/30 and 18/30. Now, we can easily select five consecutive numerators that lie between 12 and 18.Read more
To find 5 rational numbers between 2/5 and 3/5, we can scale up the fractions to have a larger common denominator. Multiplying the numerator and denominator of both fractions by 6 transforms them into 12/30 and 18/30. Now, we can easily select five consecutive numerators that lie between 12 and 18. This gives the five required rational numbers: 13/30, 14/30, 15/30, 16/30, and 17/30.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
See lessFind 6 rational numbers between 3 and 4.
To locate 6 rational numbers between the whole numbers 3 and 4, we rewrite them as equivalent fractions with a common denominator greater than 6, such as 7. This transforms 3 into 21/7 and 4 into 28/7. Now, we can choose any six consecutive fractional values that lie between these two new boundary pRead more
To locate 6 rational numbers between the whole numbers 3 and 4, we rewrite them as equivalent fractions with a common denominator greater than 6, such as 7. This transforms 3 into 21/7 and 4 into 28/7. Now, we can choose any six consecutive fractional values that lie between these two new boundary points. The resulting six rational numbers are 22/7, 23/7, 24/7, 25/7, 26/7, and 27/7.
For more NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 3 The world of numbers (2026-27):
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-3/
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