Question

x^2-12x+a=(x+b)^2 find the value of a and b

Answer 1

Answer:

x^2-12x+a=(x-6)^2

so,a=36

(x-6)^2=(x+b)^2

so,b=-6

Answer 2

SOLUTION

GIVEN

$\sf {x}^{2} - 12x + a = {(x + b)}^{2}$

TO DETERMINE

The value of a and b

EVALUATION

Here it is given that

$\sf {x}^{2} - 12x + a = {(x + b)}^{2}$

We find the value of a and b as below

$\sf {x}^{2} - 12x + a = {(x + b)}^{2}$

$\sf \implies \: {x}^{2} - 12x + a = {x}^{2} + 2bx + {b}^{2}$

$\sf \implies \: {x}^{2} + 2bx + {b}^{2} = {x}^{2} - 12x + a$

Comparing both sides we get

2b = - 12 and b² = a

2b = - 12 gives b = - 6

Again b² = a gives

$\sf a = {b}^{2}$

$\sf \implies \: a = {( - 6)}^{2}$

$\sf \implies \: a =36$

FINAL ANSWER

a = 36 , b = - 6

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