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Algebra and Applications Test 3

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Question : 3 of 25

Marks: +1, -0

If

a^2 + b^2 = 5ab

, then the value of

\left(\frac{a^2}{b^2}+\frac{b^2}{a^2}\right)

is

16
23
-23
32

Solution:

Concept:

Use algebraic identities to simplify the symmetric ratio.

Explanation:

Given

a^2+b^2=5ab

.

Square both sides:

(a^2+b^2)^2=(5ab)^2

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

So,

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

Now,

\frac{a^2}{b^2}+\frac{b^2}{a^2}=\frac{a^4+b^4}{a^2b^2}

Substitute the value:

=\frac{23a^2b^2}{a^2b^2}=23

Answer:

The value is

23

, so the correct option is B.

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