The value of 4-5-4-5-4-5-4-5-11-2342-1142-100

The correct option is B 42/114+√(5)/4 √(5)+4 √(5)/4+√(5) =(4+√(5))^2+(4 √(5))^2/(4+√(5))(4 √(5)) =(16+5+8√(5))+(16+5 8√(5))/16 5 =42/11 ...

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Byju's Answer

Standard IX

Mathematics

Operations on Rational and Irrational numbers

The value of ...

Question

The value of $\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}$

\frac{42}{11}

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\frac{11}{23}

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\frac{42}{10}

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Solution

The correct option is A $\frac{42}{11}$
$\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}} = \frac{(4 + \sqrt{5})^{2} + (4 - \sqrt{5})^{2}}{(4 + \sqrt{5}) (4 - \sqrt{5})} = \frac{(16 + 5 + 8 \sqrt{5}) + (16 + 5 - 8 \sqrt{5})}{16 - 5} = \frac{42}{11}$

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The general form of 456 is

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D. (6 × 100) + (5 × 10) + (4 × 1)

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(4) (−3)⁴

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$⎡ ⎢ ⎣ \begin{matrix} 2 & 3 & 4 3 & 4 & 5 4 & 5 & 6 \end{matrix} ⎤ ⎥ ⎦$ $⎡ ⎢ ⎣ \begin{matrix} 1 & - 3 & 5 0 & 2 & 4 3 & 0 & 5 \end{matrix} ⎤ ⎥ ⎦$

The value of $\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}$

Q. Simplify:

\frac{\sqrt{4} + \sqrt{5}}{\sqrt{4} - \sqrt{5}} + \frac{\sqrt{4} - \sqrt{5}}{\sqrt{4} + \sqrt{5}} = - m

then the value of

m

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The value of 4+√54−√5+4−√54+√5

The correct option is A 42114+√54−√5+4−√54+√5=(4+√5)2+(4−√5)2(4+√5)(4−√5)=(16+5+8√5)+(16+5−8√5)16−5=4211

The value of $\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}}$

The correct option is A $\frac{42}{11}$
$\frac{4 + \sqrt{5}}{4 - \sqrt{5}} + \frac{4 - \sqrt{5}}{4 + \sqrt{5}} = \frac{(4 + \sqrt{5})^{2} + (4 - \sqrt{5})^{2}}{(4 + \sqrt{5}) (4 - \sqrt{5})} = \frac{(16 + 5 + 8 \sqrt{5}) + (16 + 5 - 8 \sqrt{5})}{16 - 5} = \frac{42}{11}$