Question

If 3x²+8ax+3 is perfect square ,then find value of a

Answer 1

Let 3x²+8ax+3 be a perfect square . So, it is in the form of p²+2pq +q²

Comparing 3x²+8ax+3 with p²+2pq+q²

We get ,

3x² = p²

8ax = 2pq

3 = q²

From first equation,

3x² = p²

√3x = p

From third equation ,

3 = q²

√3 =q

So , Substitute p ,q in second equation

8ax = 2pq

8ax = 2 (√3x )(√3)

8ax = 2(3x)

8ax = 6x

a = 6/8

a = 3/4

If we compare the equation with (p-q)² ,We get a = -3/4

So we can conclude a = ±3/4