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The value of (1.8)3−(1.2)3(1.8)2+2.16+(1.2)2\frac{(1.8)^3 - (1.2)^3}{(1.8)^2 + 2.16 + (1.2)^2}(1.8)2+2.16+(1.2)2(1.8)3−(1.2)3​​ is:
Question

The value of (1.8)3(1.2)3(1.8)2+2.16+(1.2)2\frac{(1.8)^3 - (1.2)^3}{(1.8)^2 + 2.16 + (1.2)^2}​ is:

A.

3

B.

1.8

C.

0

D.

0.6

Correct option is D

Given:
(1.8)3(1.2)3(1.8)2+2.16+(1.2)2\frac{(1.8)^3 - (1.2)^3}{(1.8)^2 + 2.16 + (1.2)^2} \\ 
Formula Used:
a3b3a2+ab+b2=ab\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b \\ 
Solution:
=>(1.8)3(1.2)3(1.8)2+2.16+(1.2)2=>(1.8)3(1.2)3(1.8)2+1.8×1.2+(1.2)2Let a=1.8, b=1.2Apply identity: a3b3a2+ab+b2=ab=>ab=1.81.2=0.6\Rightarrow \frac{(1.8)^3 - (1.2)^3}{(1.8)^2 + 2.16 + (1.2)^2} \\\Rightarrow \frac{(1.8)^3 - (1.2)^3}{(1.8)^2 +1.8 \times 1.2 + (1.2)^2} \\\text{Let } a = 1.8,\ b = 1.2 \\\text{Apply identity: } \frac{a^3 - b^3}{a^2 + ab + b^2} = a - b \\\Rightarrow a - b = 1.8 - 1.2 = 0.6 \\
The correct answer is 0.6​

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