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

Find the values of 'a' and 'b' in each of the following: 
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x²

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find : y²

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :  xy

If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2]`; find:

x² + y² + xy.

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find m²

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find n²

If m = `1/[ 3 - 2sqrt2 ] and n = 1/[ 3 + 2sqrt2 ],` find mn

If x = `2sqrt3 + 2sqrt2`, find: `1/x`

If x = 2√3 + 2√2, find: `(x + 1/x)`

If x = 2√3 + 2√2 , find : `( x + 1/x)^2`

If x = 1 - √2, find the value of `( x - 1/x )^3`

If x = 5 - 2√6, find `x^2 + 1/x^2`

Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`

If `[ 2 + sqrt5 ]/[ 2 - sqrt5] = x and  [2 - sqrt5 ]/[ 2 + sqrt5] = y`; find the value of x² - y².

Evaluate: `( 4 - √5 )/( 4 + √5 ) + ( 4 + √5 )/( 4 - √5 )`

If √2 = 1.4 and √3 = 1.7, find the value of : `1/(√3 - √2)`

If √2 = 1.4 and √3 = 1.7, find the value of : `1/(3 + 2√2)`

Factorise:

a³ - 27