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Question

The value of (1.5)3+(4.7)3+(3.8)33×1.5×4.7×3.8(1.5)2+(4.7)2+(3.8)21.5×4.74.7×3.81.5×3.8 is

A
0
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B
1
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C
10
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D
30
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Solution

The correct option is C 10
We know that one of the identity of polynomials is:
a3+b3+c33abc=(a+b+c)(a2+b2+c2abbcca)
Now let us substitute a=1.5,b=4.7 and c=3.8 in the above identity as follows:
(1.5)3+(4.7)3+(3.8)33×1.5×4.7×3.8
=(1.5+4.7+3.8){(1.5)2+(4.7)2+(3.8)2(1.5×4.7)
(4.7×3.8)(1.5×3.8)} .....(1)
Now consider the given expression as shown below:
(1.5)3+(4.7)3+(3.8)33×1.5×4.7×3.8(1.5)2+(4.7)2+(3.8)2(1.5×4.7)(4.7×3.8)(1.5×3.8)

=(1.5+4.7+3.8){(1.5)2+(4.7)2+(3.8)2(1.5×4.7)(4.7×3.8)(1.5×3.8)}(1.5)2+(4.7)2+(3.8)2(1.5×4.7)(4.7×3.8)(1.5×3.8) ....From eq(1)
=1.5+4.7+3.8=10

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