Question

If a-b = 7 and a3 - b3 = 133, then find the value of a2 + b2 *

29

92

-29

63​

Answer 1

Answer:

Step-by-step explanation:

a^3-b^3=(a-b)(a^2+ab+b^2)

133=(7)(a^2+ab+b^2)

19=(a^2+ab+b^2)

a^2+b^2=

WE KNOW A-B=7

a=7+b

sub, 19=(7+b)^2+(7+b)b+b^2

19=49+b^2+14b+7b+b^2+b^2

on solving,

if b=-2,a=5

if b=-5, a=2(but the second is not possible, since a-b is not equal to seven)

thus a=5,b=-2

on substituting,

a2 + b2=29