Practice Questions on Simplification

Question of The Day02-11-2020

What is the value of \((6.7)^4+(3.9)^4+(26.13)^2\over (6.7)^2+(3.9)^2+26.13\)?

Answer

Correct Answer : c ) 33.97

Explanation :

Consider the given expression

\((6.7)^4+(3.9)^4+(26.13)^2\over (6.7)^2+(3.9)^2+26.13\)

Let us assume a = 6.7, b = 3.9

Thus, ab = 6.7 × 3.9 = 26.13

Thus,

\((a)^4+(b)^4+(ab)^2\over (a)^2+(b)^2+ab\)

⇒\((a^2)^2+(b^2)^2+2(ab)^2-(ab)^2\over (a)^2+(b)^2+ab\)

⇒\((a+b)^2-(ab)^2\over (a)^2+(b)^2+ab\)

We know that, x² – y² = (x – y) (x + y)

⇒\({(a+b+ab)(a^2+b^2-ab)\over (a^2+b^2+ab)}= (a^2+b^2-ab)\)

⇒\( (a^2+b^2-2ab+ab)\)

We know,

(x – y)² = x² + y² – 2xy

⇒\( ((a-b)^2+ab)\)

⇒\( (6.7-3.9)^2+26.13\)

⇒ 2.8² + 26.13

⇒ 33.97

Hence, (c) is the correct answer.

Such type of question is asked in various government exams like SSC CGL, SSC MTS, SSC CPO, SSC CHSL, RRB JE, RRB NTPC, RRB GROUP D, RRB OFFICER SCALE-I, IBPS PO, IBPS SO, RRB Office Assistant, IBPS Clerk, RBI Assistant, IBPS RRB OFFICER SCALE 2&3, UPSC CDS, UPSC NDA, etc.

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