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IBPS Clerk Prelims Model Paper 10

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Question : 1 of 100

Marks: +1, -0

\frac{137\times 137+137\times 133+133\times 133}{137\times 137\times 137-133\times 133\times 133}

= ?

4
270
$\frac{1}{4}$
$\frac{1}{270}$
None of these

Solution:

Concept:

Apply the identity

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

to simplify the expression.

Explanation:

Let

a=137

and

b=133

.

The numerator is

a^2+ab+b^2

.

The denominator is

a^3-b^3

.

Factor the denominator:

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

.

Cancel the common factor

a^2+ab+b^2

.

The expression becomes

\frac{1}{a-b}

.

Substitute the values:

\frac{1}{137-133}=\frac{1}{4}

.

Answer:

\frac{1}{4}

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