If a^2 + b^2 = 5ab, then the value of (a^2/b^2+b^2/a^2) is

Algebra and Applications Test 3

Question : 3 of 25

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a^2 + b^2 = 5ab

, then the value of

(a^2/b^2+b^2/a^2)

Solution:

a^2 + b^2 = 5ab

Squaring both sides, we get:

a^4 + b^4 + 2a^2b^2 = 25a^2b^2

a^4 + b^4 = 23a^2b^2

Now,

(a^2/b^2+b^2/a^2)=({a^4+b^4}/{a^2b^2})

={23a^2b^2}/{a^2b^2}=23

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