1.

The value of \(\frac{[(1.3)^2+(1.3\times1.5)+(1.5)^2]\times[(1.3)^2-1.95+(1.5)^2]}{(1.3)^4+(1.3)^2(2.25)+(1.5)^4}\) is:

Answer» Correct Answer - Option 3 : 1

Given: 

\(\frac{[(1.3)^2+(1.3\times1.5)+(1.5)^2]\times[(1.3)^2-1.95+(1.5)^2]}{(1.3)^4+(1.3)^2(2.25)+(1.5)^4}\)

Concept used:

The numerator of the given expression is of the form = (a2 + ab + b2) × (a2 – ab + b2)

Expanding and solving we get:

(a2 + ab + b2) × (a2 – ab + b2) = a4 – a3b + a2b2 + a3b – a2b2 + ab3 + a2b2 – ab3 + b4

⇒ (a2 + ab + b2) × (a2 – ab + b2) = a4 + a2b2 + b4

Denominator is of the form = a4 + a2b2 + b4

Calculation:

Numerator:

[(1.3)2 + (1.3 × 1.5) + (1.5)2] × [(1.3)2 – 1.95 + (1.5)2] = [(1.3)2 + (1.3 × 1.5) + (1.5)2] × [(1.3)2 – (1.3 × 1.5) + (1.5)2]

⇒ [(1.3)2 + (1.3 × 1.5) + (1.5)2] × [(1.3)2 – (1.3 × 1.5) + (1.5)2] = (1.3)4 + (1.3)2 × (1.5)2 + (1.5)4

Denominator:

(1.3)4 + (1.3)2 (2.25) + (1.5)4 = (1.3)4 + (1.3)2 × (1.5)2 + (1.5)4

Now, Numerator/Denominator = [(1.3)4 + (1.3)2 × (1.5)2 + (1.5)4]/ [(1.3)4 + (1.3)2 × (1.5)2 + (1.5)4]

⇒ Numerator/Denominator = 1

∴ The value of the given expression is 1.


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