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a,b are positive real numbers if a2+b2+22 and a4+b4=386 find the value of(a3+b3)

a,b are positive real numbers if a2+b2+22 and a4+b4=386
find the value of(a3+b3)

Grade:10

1 Answers

Ajay Verma
askIITians Faculty 33 Points
10 years ago
soln:

a^2 + b^2 = 22 (given)..................(1)
a^4 + b^4 = 386 (given)..................(2)

{a^2 + b^2 }^2= 484 (from eqn 1)
a^4 + b^4 + 2 a^2 b^2 = 484
386 + 2 a^2 b^2 = 484
a^2 b^2 = 49
ab = 7


now..
(a+b)^2 = a^2 + b^2 + 2ab
(a+b)^2 = 22 + 2*7
a+b = 6................ (3)


a^3 + b^3 = (a+b)(a^2 - ab + b^2)
a^3 + b^3 = 6 *(22 - 7)
a^3 + b^3= 6 * (15)
a^3 + b^3= 90



Thanks and Regards,
Ajay verma,
askIITians faculty,
IIT HYDERABAD





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