If a + b is equal to 5 and a square + b square is equal to 11 then prove that a cube plus b cube is equal to 20 answer
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Answer:
a+b=5
a^2+b^2=11
a^3++b^3=(a+b)(a^2-ab+b^2)
we know that (a+b)^2 =a^2+b^2+2ab
from above eqn ...25-11=2ab
ab=7
a^3+b^3=5(11-7)
=5(4)=20
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GIVEN - a+b=5
a^2+b^2=11
TO PROOF- a^3+b^3=20
a+b=5
a^2+b^2=11
(a+b)^2= a2 +b2 +2ab
=> 5^2 = 11 +2ab
=> 25 - 11 =2ab
=> 2ab =14
=> ab = 14/2 = 7
=>ab =7
a3 + b3 =(a+b)3 - 3ab(a+b)
= 125 - 105 = 20
.°. a^3+b^3 = 20
HENCE PROVED
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