Advertisements
Advertisements
Question
If x =`[sqrt5 - 2 ]/[ sqrt5 + 2]` and y = `[ sqrt5 + 2]/[ sqrt5 - 2 ]`; find :
x2
Advertisements
Solution
x2 = `[( sqrt5 - 2 )/( sqrt5 + 2 )]^2 = [ 5 + 4 - 4sqrt5 ]/[ 5 + 4 + 4sqrt5] = [ 9 - 4sqrt5 ]/[ 9 + 4sqrt5 ]`
= `[ 9 - 4sqrt5 ]/[ 9 + 4sqrt5 ] xx [( 9 - 4sqrt5 )/( 9 - 4sqrt5 )] = (9 - 4sqrt5)^2/[(9)^2 - (4sqrt5)^2]`
= `[ 81 + 80 - 72sqrt5]/[ 81 - 80 ] = 161 - 72sqrt5 `
APPEARS IN
RELATED QUESTIONS
Write the lowest rationalising factor of : √24
Write the lowest rationalising factor of : √18 - √50
If x = 1 - √2, find the value of `( x - 1/x )^3`
If x = 5 - 2√6, find `x^2 + 1/x^2`
If √2 = 1.4 and √3 = 1.7, find the value of : `1/(√3 - √2)`
Rationalise the denominator `1/sqrt(50)`
Rationalise the denominator `(3sqrt(5))/sqrt(6)`
Rationalise the denominator and simplify `sqrt(5)/(sqrt(6) + 2) - sqrt(5)/(sqrt(6) - 2)`
Find the value of a and b if `(sqrt(7) - 2)/(sqrt(7) + 2) = asqrt(7) + b`.
If x = `sqrt(5) + 2`, then find the value of `x^2 + 1/x^2`
