Question

if x² + 1/x²=6 find the value x⁴+1/x⁴

Answer 1

( x^2 + 1/x^2 ) = 6

Square on both sides,

( x^2 + 1/x^2 )^2 = 6^2

$\mathbf{ we \; know, ( a + b )^2 = a^2 + b^2 + 2ab }$

=> ( x^2 )^2 + ( 1/x^2 )^2 + 2( x^2 × 1/x^2 ) = 36

=> x^4 + 1/x^4 + 2 ( 1 ) = 36

=> x^4 + 1/x^4 = 36 - 2

=> x^4 + 1/x^4 = 34

Answer 2

given x^2+1/x^2=6
squaring on both sides
we get,
x^4+1/x^4+2= 36
x^4+1/x^4= 36-2
= 34
hope this helps you...