(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If a² + b² = 34 and ab = 12; find : 7(a - b)² - 2(a + b)²

If 3x - `4/x` = 4; and x ≠ 0 find : 27x³ - `64/x^3`

If x² + `x^(1/2)`= 7 and  x ≠ 0; find the value of: 
7x³ + 8x − `7/x^3 - 8/x`

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : Their product

The difference between two positive numbers is 4 and the difference between their cubes is 316.
Find : The sum of their squares

If `(x^2 + 1)/x = 3 1/3` and x > 1; Find `x - 1/x`.

If `(x^2 + 1)/x = 3 1/3` and  x > 1; find If `x^3 - 1/x^3`

Find the value of 'a':  4x² + ax + 9 = (2x + 3)²

Find the value of 'a': 4x² + ax + 9 = (2x - 3)²

Find the value of 'a': 9x² + (7a - 5)x + 25 = (3x + 5)²

The sum of two numbers is 7 and the sum of their cubes is 133, find the sum of their square.

If 3a + 5b + 4c = 0, show that : 27a³ + 125b³ + 64c³ = 180 abc

If x = `1/[ 5 - x ]  "and x ≠ 5 find "x^3 + 1/x^3`

If x = `1/( x - 5 ) "and x ≠ 5. Find" : x^2 - 1/x^2`

Factorise by taking out the common factors : 
2 (2x - 5y) (3x + 4y) - 6 (2x - 5y) (x - y)

Factories by taking out common factors :
xy(3x² - 2y²) - yz(2y² - 3x²) + zx(15x² - 10y²)

Factories by taking out common factors :
ab(a² + b² - c²) - bc(c² - a² - b²) + ca(a² + b² - c²)

Factories by taking out common factors :
2x(a - b) + 3y(5a - 5b) + 4z(2b - 2a)

Factorise:

`x^2 + 1/(4x^2) + 1 - 7x - 7/(2x)`

Factorise : `(9a)^2 + 1/(9a)^2 - 2 - 12a + 4/(3a)`