Question

What should be added to 4a⁴+ 4a³ + 5a² + 2a +5 to make it a perfect square ?​

Answer 1

Step-by-step explanation:

4a^4+4a^3+5a^2+2a+5+x

={(2a^2)^2+2.2a^2.a+a^2}+{(2a)^2+2.2a.1+(1)^2}-2a+4+x

=(2a^2+a)^2+(2a+1)^2+(4-2a+x)

.°. 4-2a+x=0

or,x= -2a-4

= -(2a+4)

.°.-(2a+4) should be added to make the equation a perfect square.(Ans.)

Answer 2

Answer:

-(2a+4)

Step-by-step explanation:

Let we add x to make a perfect square

4$a^{4}$+4a³+5a²+2a+5+x = 0

{(2a²)²+2.(2a²)(a)+a²} + {(2a)²+2(2a)(1)+(1)²} -2a+4+x = 0

(2a²+a)² + (2a+1)² + (4-2a+x) = 0

So 4-2a+x should be zero to make it a perfect square.

4-2a+x = 0

∴ x= -2a-4 = -(2a+4)

∴ We have to add -(2a+4) to make a perfect square.

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