Solve: 1 x 2 - 6 = 2 x 2 + 2

Given, 1 x 2 - 6 = 2 x 2 + 2 We need to simplify and solve the equation. Cross multiplying, we get 1 x 2 + 2 = 2 x 2 - 6 x 2 + 2 = 2 x 2 - 12 Taking the variable to R.H.S and constant term to L.H.S 2 + 12 = 2 x 2 - x 2 14 = x 2 Taking square root on both sides, we get x 2 = 14 x = ± 14 Hence, the required answer is as shown above.

Solve: 1 x 2 - 6 = 2 x 2 + 2

Given, 1 x 2 - 6 = 2 x 2 + 2 We need to simplify and solve the equation. Cross multiplying, we get 1 x 2 + 2 = 2 x 2 - 6 x 2 + 2 = 2 x 2 - 12 Taking the variable to R.H.S and constant term to L.H.S 2 + 12 = 2 x 2 - x 2 14 = x 2 Taking square root on both sides, we get x 2 = 14 x = ± 14 Hence, the required answer is as shown above.

Solve: x 2 x 2 + 2 + x 2 - 5 x 2 - 6 = 2

Given, x 2 x 2 + 2 + x 2 - 5 x 2 - 6 = 2 We need to simplify and solve the equation. x 2 x 2 - 6 + x 2 - 5 x 2 + 2 x 2 + 2 x 2 - 6 = 2 x 4 - 6 x 2 + x 4 + 2 x 2 - 5 x 2 - 10 x 4 + 2 x 2 - 6 x 2 - 12 = 2 2 x 4 - 9 x 2 - 10 x 4 - 4 x 2 - 12 = 2 1 Cross multiply, we get 2 x 4 - 9 x 2 - 10 = 2 x 4 - 4 x 2 - 12 2 x 4 - 9 x 2 - 10 = 2 x 4 - 8 x 2 - 24 2 x 4 - 9 x 2 - 10 = 2 x 4 - 8 x 2 - 24 - 9 x 2 + 8 x 2 = - 24 + 10 - x 2 = - 14 x 2 = 14 x = ± 14 Hence, the required answer is as shown above.

Solve: x - 2 x + 2 + x + 2 x - 2 = 5 2

Given, x - 2 x + 2 + x + 2 x - 2 = 5 2 We need to simplify and solve the equation. x - 2 x - 2 + x + 2 x + 2 x + 2 x - 2 = 5 2 x - 2 2 + x + 2 2 x + 2 x - 2 = 5 2 x - 2 2 + x + 2 2 x 2 - 2 2 = 5 2 x 2 + 4 - 4 x + x 2 + 4 + 4 x x 2 - 4 = 5 2 2 x 2 + 8 x 2 - 4 = 5 2 Cross multiplying, we get 2 2 x 2 + 8 = 5 x 2 - 4 4 x 2 + 16 = 5 x 2 - 20 4 x 2 - 5 x 2 = - 20 - 16 - x 2 = - 36 x 2 = 36 Taking square root on both sides, we get x 2 = 36 x = ± 6 Hence, the required answer is as shown above.