Question

Solve the equation √x²-1 =√3

Answer 1

Given that

x = 2 + √3

1/x = 1/2 + √3

= 1 × (2 - √3)/(2 + √3) (2 - √3)

= (2 - √3)/(2^2 - √3^2)

= (2 - √3)/4 - 3

= (2 - √3)

Therefore ,

x^2 = (2 + √3)

= (2)^2 + (√3)^2 + 2 × 2 × √3

= 4 + 3 + 4√3

= 7 + 4√3

1/x^2 = (2 - √3)^2

= (2)^2 + (√3)^2 - 2 × 2 × √3

= 4 + 3 - 4√3

= 7 - 4√3

x^2 + 1/x^2

= (7 + 4√3) + (7 - 4√3)

= 7 + 4√3 + 7 - 4√3

= 7 + 7 + 4√3 - 4√3

= 14

Answer 2

Step-by-step explanation:

Given Value

√x²-1 =√3

Squaring both sides

(✓x²-1)²=(✓3)²

x²+1-2x=3

x²+2x-2=0

x²+x+x-2=0

x=2 or x=1

Hope it helps you mate