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The value of 0.663−0.2230.662+0.1452+0.222\frac{0.66^3 - 0.22^3}{0.66^2 + 0.1452 + 0.22^2}0.662+0.1452+0.2220.663−0.223​​is:
Question

The value of 0.6630.2230.662+0.1452+0.222\frac{0.66^3 - 0.22^3}{0.66^2 + 0.1452 + 0.22^2}​is:

A.

100

B.

1

C.

0.44

D.

10

Correct option is C

Given
Expression = 0.6630.2230.662+0.1452+0.222\frac{0.66^3 - 0.22^3}{0.66^2 + 0.1452 + 0.22^2}​​
Formula Used
a3b3=(ab)(a2+ab+b2)a^3 - b^3 = (a - b)(a^2 + ab + b^2)​​
Solution
Let a = 0.66 and b = 0.22.
Notice that a × b = 0.66 × 0.22 = 0.1452.
The given expression is in the form a3b3a2+ab+b2. \frac{a^3 - b^3}{a^2 + ab + b^2}.​​
Using the algebraic identity, the expression simplifies to (a - b).
= 0.66 - 0.22
= 0.44
Final Answer
So the correct answer is (c)

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