Question

Find the values of p and q such that

4x² + 12x = 4( x + p²) - q




Subject - Completing the square - Maths

I NEED HELP PLEASE :(

Answer 1

Answer:

Step-by-step explanation:

I may perhaps be mistaking but i think the question should be: "For what value of  

c

will the expression  

4

x

2

+

12

x

+

c

be a perfect square?"

In that case here's my solution:

That expression must be in the  

(

a

x

+

b

)

2

for it to be a perfect square, so i write

4

x

2

+

12

x

+

c

≡

(

a

x

+

b

)

2

⇒

4x^2 + 12x + c-= a^2x^2 + 2abx + b^2#

Equating coefficients of the powers of  

x

on both sides,

4

=

a

2

⇒

a

2

=

4

12

=

2

a

b

⇒

4

a

2

b

2

=

144

⇒

4

⋅

4

⋅

b

2

=

144

⇒

b

2

=

9

c

=

b

2

⇒

c

=

9