{(598+479)²-(598-479)²}{598× 479}= ?

None of the above/More than one of the above

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BPSC 66th Prelims 27 Dec 2020 Paper

Question : 149 of 150

Marks: +1, -0

\frac{(598+479)^{2}-(598-479)^{2}}{598\times 479}= ?

Solution:

Concept:

Use the identity

(a+b)^2 - (a-b)^2 = 4ab

. This simplifies the numerator directly.

Explanation:

Let

a = 598

and

b = 479

. The numerator is

(a+b)^2 - (a-b)^2

Expand:

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

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

Subtracting gives

a^2 + 2ab + b^2 - a^2 + 2ab - b^2 = 4ab

The denominator is

598 \times 479 = ab

Thus the expression becomes

\frac{4ab}{ab} = 4

Answer:

Option A: 4

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