Question

(x + a)² = x² + 22x + b Find the value of a and the value of b.​

Answer 1

`a = 11 \: , \: b = 121`

Explanation:

`(x + a) {}^(2) = x {}^(2) + 22x + b`

`expanding \: (x + a) {}^(2)`

`(x + a)(x + a) = x {}^(2) + 2ax + a {}^(2)`

Equate both sides and compare coefficients;

`x {}^(2) + 2ax + a {}^(2) = x {}^(2) + 22x + b`

`x {}^(2) ; \: 1 = 1`

`x; \: 2a = 22......(i)`

`constant; \: a {}^(2) = b......(ii)`

From(i);

From(i);2a = 22

From(i);2a = 22a = 22/2

From(i);2a = 22a = 22/2a = 11

From(ii);

a² = b

11² = b

121 = b

Therefore a = 11, b = 121.

Answer 2

here you go man , just expand the bracket and then compare values that are in the same position, this concept follows the general equation of x^2+bx+c