Question

if x=2+√3,then find the value of x²+1÷x²(with steps, class 9)

Answer 1

Hiii friend,

Given :- X = (2+✓3)

Therefore,

1/X = 1/(2+✓3) = 1/(2+✓3) × (2-✓3)/(2-✓3)

=> (2-✓3)/(2+✓3)(2-✓3)


=> (2-✓3)/(2)² - (✓3)²

=> (2-✓3)/4-3 => (2-✓3)/1

=> 2-✓3



Therefore,


X + 1/X = (2+✓3) + (2-✓3) = 4


=> (X + 1/X)² = (4)² = 16

=> (X²+ 1/X²) + 2 × X × 1/X = 16

=> ( X²+1/X²) + 2 = 16

=> (X²+1/X²) = (16-2)


=> (X²+1/X²) = 14

Hence,

(X²+1/X²) = 14

HOPE IT WILL HELP YOU...... :-)