Question

Which constant must be added and subtracted to solve the quadratic equation 9x2 + 3/4x– √2 = 0 by the method of completing the square?​

Answer 1

Given, the quadratic equation is 9x² + (3/4)x - √2 = 0

We have to find the constant to be added and subtracted to solve the quadratic equation by the method of completing the square.

Let y = 3x

Now, (3x)² + (3x)/4 - √2 = 0

y² + (1/4)y - √2 = 0 --------------------- (1)

By using algebraic identity,

(a + b)² = a² + 2ab + b² --------------------- (2)

Comparing (1) and (2),

a² = 1

a = 1

2ab = 1/4

2(1)b = 1/4

b = 1/8

b² = (1/8)² = 1/64

So, y² + (1/4)y - √2 + 1/64 - 1/64 = 0

On rearranging,

y² + (1/4)y + 1/64 - √2 - 1/64 = 0

(y + 1/8)² = √2 + 1/64

Now, (3x + 1/8)² = √2 + 1/64

Therefore, the constant to be added and subtracted is 1/64.