Find the value of the expression: $ 3\; + \; 5 3\; - \; 5 - \; 3\; - \; 5 3\; + \; 5 = \;?$

ক) 3√5 — Given expression is, $ array l 3\; + \; 5 3\; - \; 5 - \; 3\; - \; 5 3\; + \; 5 \\ = \; ( 3\; + \; 5 ) ^2 - \; ( 3\; - \; 5 ) ^2 ( 3\; - \; 5 ) ( 3 + 5 ) \\ = \; ( 9\; + \;5\; + \;6 5 ) - \; ( 9\; + \;5\; - 6\; 5 ) ( 3 ) ^2 - \; ( 5 ) ^2 \\ = 12\; 5 9 - 5 array $ = 12√5/4 = 3√5

Find the value of the expression: \( 3\;… | Answer

Subject

Quantitative Aptitude

Topic

Simplification

Find the value of the expression: $\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?$
Reading

ক)

3√5

খ)

-4√5

গ)

-3√5

ঘ)

4√5

ঙ)

None of these

Explanation

Given expression is,

\begin{array}{l} \frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }}\\ = \;\frac{{{{\left( {3\; + \;\sqrt 5 } \right)}^2} - \;{{\left( {3\; - \;\surd 5} \right)}^2}}}{{\left( {3\; - \;\sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)}}\\ = \;\frac{{\left( {9\; + \;5\; + \;6\sqrt 5 } \right) - \;\left( {9\; + \;5\; - 6\;\sqrt 5 } \right)}}{{{{\left( 3 \right)}^2} - \;{{\left( {\sqrt 5 } \right)}^2}}}\\ = \frac{{12\;\sqrt 5 }}{{9 - 5}} \end{array}

= 12√5/4 = 3√5

The difference of 1 (3/16) and its reciprocal is equal to What should come in place of question mark (?) in the following question? (43% of 2750) – (38% of 2990) =?How many (1/8)s are there in 37 (1/2)?If

x = \sqrt {\left( {1.96} \right)} - \sqrt {\left( {0.04} \right)}

then the value of x is Find the value -2+(-2)-{-(2)}-2 Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4). The maximum value among the above three is What will come in place of the question mark (?) in the following equation? 160 km 80 m ÷ 6 = ?If I = (3/4) ÷ (5/6), II = 3 ÷ [(4 ÷ 5) ÷ 6], III = [3 ÷ (4 ÷ 5)] ÷ 6, IV = 3 ÷ 4 ÷ (5 ÷ 6), then

Find the value of the expression: 3 + 53 − 5− 3 − 53 + 5= ?\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?3−5​3+5​​−3+5​3−5​​=?Reading

Find the value of the expression: 3 + 53 − 5− 3 − 53 + 5= ?\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?3−5​3+5​​−3+5​3−5​​=?

Explanation

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Find the value of the expression: $\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?$
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Find the value of the expression: $\frac{{3\; + \;\sqrt 5 }}{{3\; - \;\sqrt 5 }} - \;\frac{{3\; - \;\sqrt 5 }}{{3\; + \;\sqrt 5 }} = \;?$