Question

what should be added to x^2+x to make it a perfect square?​

Answer 1

Answer:

$\frac{1}{4}$

Step-by-step explanation:

Using Idiom

$(x+y)^2= x^2 + 2xy + y^2$

Given expression is:

$x^{2} +x$ $= x^{2} +2.x.\frac{1}{2}$

adding $\frac{1}{4}$ to the above expression will make it a perfect square

$= x^2+2.x.\frac{1}{2} + (\frac{1}{2}) ^{2}\\= (x + \frac{1}{2} )^2$

Answer 2

*Question:—

what should be added to x²+x to make it a perfect square?

*Answer:—

We need to add 1/4(c²) to the expression x² + x to make it a perfect square.

*Step by Step explanation:—

Let the unknown constant value be c², that will make it a perfect square.

• → x² + x + c²

Comparing this to a perfect square, that is, a² + 2ab + b²,

We get,

• → x = 2ab,
• → x = a, c = b

The value of b comes out to be equal to 1/2 which is also equal to c.

Therefore,

We need to add 1/4(c²) to the expression x² + x to make it a perfect square.

$@vikramjeeth$