Question

if x = 1/(square root(2) -1 ) then prove that x^2 - 6 + 1/x^2 = 0

Answer 1

Step-by-step explanation:

Answer refers to picture

Answer 2

Answer:

Step-by-step explanation:

x= 1/√2-1

= 1/(√2-1) × (√2+1)(√2-1) = (√2+1) / (√2)² -(1)² = (√2+1) / 2-1_(√2+1) / 1 = (√2+1)

x² = (√2+1)²=(√2)²+2 × √2 × 1 +(1)² = 2+2√2+1=3+2√2

1/x² = 1/(3+2√2)

= 1/(3+2√2) / (3-2√2)(3-2√2)=(3-2√2) / (3)²- (2√2)²=(3-2√2) / 9-8= (3-2√2) /1=(3-2√2)

∴ x² - 6 + 1/x² = 3 + 2√2 - 6 + 3 - 2√2= 6 - 6 + 2√2 - 2√2 = 0 is proved.