Find the value of -a- in 5 - 3-2-5 - 3-2 - a - b -2- then a - m-7 where m is rational number-

We rationalize the denominator 5+3√( 2 ) #160; 5 3√( 2 ) #160;× 5+3√( 2 ) #160; 5+3√( 2 ) #160; = 25+18+30√( 2 ) #160; 25 18 = 4 ...

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Algebraic Identities

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Question

Find the value of 'a' in $\frac{5 + 3 \sqrt{2}}{5 - 3 \sqrt{2}} = a + b \sqrt{2}$ , then $a = \frac{m}{7}$ where m is rational number.

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\frac{22}{2 \sqrt{3} + 1} + \frac{17}{2 \sqrt{3} - 1}

\frac{78 \sqrt{3} - 5}{m}

If a and b are rational numbers, find the values of a and b in the following equality

5+2√3 ÷7+4 √3 = a + b √ 3

{[{(\frac{- 7}{3})}^{2}]}^{5}

{(\frac{- 3}{7})}^{- m}

(- m)

In each of the following determine rational numbers a and b :

(i) $\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = a - b \sqrt{3}$

(ii) $\frac{4 + \sqrt{2}}{2 + \sqrt{2}} = a - \sqrt{b}$

(iii) $\frac{3 + \sqrt{2}}{3 - \sqrt{2}} = a + b \sqrt{2}$

(iv) $\frac{5 + 3 \sqrt{3}}{7 + 4 \sqrt{3}} = a + b \sqrt{3}$

(v) $\frac{\sqrt{11} - \sqrt{7}}{\sqrt{11} + \sqrt{7}} = a - b \sqrt{77}$

(vi) $\frac{4 + 3 \sqrt{5}}{4 - 3 \sqrt{5}} = a + b \sqrt{5}$

\frac{\sqrt{7} - 2}{\sqrt{7} + 2} = a \sqrt{7} + b

a = - \frac{m}{3}

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