Question

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The difference of two numbers is 8. If the sum of the smaller number and the square of the larger number is 148, what is the smaller number?

Answer 1

Answer: The smaller number is -21 or 4

Step-by-step explanation:

Let the smaller number be y and the larger number be x , then

x - y = 8 ..................... equation 1

From the second statement

$x^{2} +y = 148$ .................... equation 2

combining the two equations:

$x - y = 8$ .......................equation 1

$x^{2} + y = 148$  .................... equation 2

solving the system of equation by substitution method , from equation 1 , make y the subject of the formula.

$y = x - 8$ ...................... equation 3

substitute equation 3 into equation 2 , we have

$x^{2} +x - 8 = 148$

$x^{2} +x - 8 - 148 = 0$

$x^{2} +x-156=0$

Factorizing the quadratic expression , we have

$(x+13)(x-12) = 0$

That is

$x =- 13$ or $x= 12$

When  $x = -13$ , $y = -13 - 8$

$y = -21$                    (-13 , -21 )

when $x = 12$ , $y = 12 - 8$

$y = 4$                       ( 12 ,4 )

Check:

-13 - (-21)

-13 + 21 = 8

$(-13)^{2} -21 = 148$

Also

12 - 4 = 8

$12^{2} + 4 = 148$

Therefore , the smaller number is -21 or 4

Answer 2

The numbers are 12 and 4. If you subtract 4 from 12, you will get 8. If you add 4 to the squared 12, which is 144, you will get 148. That means the smaller number is 4.