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
[tex]x^{2} +y = 148[/tex] .................... equation 2
combining the two equations:
[tex]x - y = 8[/tex] .......................equation 1
[tex]x^{2} + y = 148[/tex] .................... equation 2
solving the system of equation by substitution method , from equation 1 , make y the subject of the formula.
[tex]y = x - 8[/tex] ...................... equation 3
substitute equation 3 into equation 2 , we have
[tex]x^{2} +x - 8 = 148[/tex]
[tex]x^{2} +x - 8 - 148 = 0[/tex]
[tex]x^{2} +x-156=0[/tex]
Factorizing the quadratic expression , we have
[tex](x+13)(x-12) = 0[/tex]
That is
[tex]x =- 13[/tex] or [tex]x= 12[/tex]
When [tex]x = -13[/tex] , [tex]y = -13 - 8[/tex]
[tex]y = -21[/tex] (-13 , -21 )
when [tex]x = 12[/tex] , [tex]y = 12 - 8[/tex]
[tex]y = 4[/tex] ( 12 ,4 )
Check:
-13 - (-21)
-13 + 21 = 8
[tex](-13)^{2} -21 = 148[/tex]
Also
12 - 4 = 8
[tex]12^{2} + 4 = 148[/tex]
Therefore , the smaller number is -21 or 4
