Question

solve this question : if a+b=10 and a^2+b^2=58 then find a^3+b^3

Answer 1

a=7
b=3

7'3+3'3=343+27
=370

Answer 2

a+b=10 , a^2+b^2=58

Find a^3+b^3

Formula for a^2+b^2=(a+b)^2-2ab

a+b=10 (given)

a^2+b^2=(10)^2-2ab

a^2+b^2=100-2ab

As, a^2+b^2=58 (given)

So, by putting the value, we get

58=100-2ab

100-58=2ab

42=2ab

42/2=ab

21=ab

Now, formula for a^3+b^3=(a+b)(a^2-ab+b^2)

a^3+b^3=(10)(a^2+b^2-ab)

a^3+b^3=(10)(58- (from above equation we get ab=21)SO,

a^3+b^3=(10)(58-21)

a^3+b^3=(10)(37)

a^3+b^3=370

PROBLEM SOLVED!!!!!