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JIPMAT 2022

Algebra

>

Identities

Easy

The value of $\frac{325 \times 325 \times 325+175 \times 175 \times 175}{325 \times 325-325 \times 175+175 \times 175}$ is

143755

1125

9575

500

✅ Correct Option: 4

The given expression can be written as:

\frac{(325)^3+(175)^3}{(325)^2+(175)^2-(325)(175)}

Let

a=325

,

b=175,

then:

\frac{a^3+b^3}{a^2+b^2-ab}

We know that

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

So:

\frac{(a+b)(a^2+b^2-ab)}{(a^2+b^2-ab)}=a+b=325+175=500

Related questions:

JIPMAT 2021

(25.732^{2} - 15.732^{2})

JIPMAT 2022

Which of the following is the value of

m

for which the polynomial

x^4 + 10x^3 + 25x^2 + 15x + m

is exactly divisible by

x+7

JIPMAT 2025

\frac{(4.53-3.07)^2}{(3.07-2.15)(2.15-4.53)} + \frac{(3.07-2.15)^2}{(2.15-4.53)(4.53-3.07)} + \frac{(2.15-4.53)^2}{(4.53-3.07)(3.07-2.15)}

is simplified to