X squared - x + 5 = (x-a) squared + b. what are the values of a and b

Question

asked Jun 16, 2022 130k views

1 Answer

Susam Pal · Answer 1 · 2022-06-21T02:30:45+0000

${x}^(2) - x + 5 = ({x - a})^(2) + b$

${x}^(2) - x + 5 = {x}^(2) + 2ax + {a}^(2) + b$

This is the equation which mean all the terms must be equalls to the like terms over the " = " peer to peer , look :

${x}^(2) = {x}^(2)$

And

- x = 2ax

And

${a}^(2) + b = 5$

_____________________________________________

Now it's time to find the a and b values ;

- x = 2ax

Divide both sides by x

$( - x)/(x) = (2ax)/(x) \\$

- 1 = 2a

Divide both sides by 2

$( - 1)/(2) = (2a)/(2) \\$

$a = - (1)/(2) \\$

♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡

${a}^(2) + b = 5$

$( { - ( 1)/(2) })^(2) + b = 5 \\$

$(1)/(4) + b = 5 \\$

Subtract both sides ¼

$(1)/(4) - (1)/(4) + b = 5 - (1)/(4) \\$

$b = (20)/(4) - (1)/(4) \\$

$b = (19)/(4) \\$

_____________________________________________

Thus :

$a = - (1)/(2) \\$

$b = (19)/(4) = 4.75 \\$

There you go...

Have a great day ❤