Answer:

Given, the quadratic equation is 4x² − √3x − 5 = 0 -------------------- (1)

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

By using algebraic identity,

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

Comparing (1) and (2),

a² = 4

a = 2

-2ab = -√3

2(2)b = √3

b = √3/4

b² = (√3/4)² = 3/16

So, 4x² - √3x - 5 + 3/16 - 3/16 = 0

(2x - √3/4)² - 5 - 3/16 = 0

(2x - 3/16)² = 5 + 3/16

(2x - 3/16)² = (80 + 3)/16

(2x - 3/16)² = 83/16

Therefore, the constant to be added and subtracted is 3/16.

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