If a-3-2-3-2 and b-3-2-3-2- If the value of a-b-5ab is -4-m-5 then find m-

a+b 5ab=√(3) √(2)/√(3)+√(2)+√(3)+√(2)/√(3) √(2) 5((√(3) √(2))(√(3)+√(2))/(√(3)+√(2))(√(3) √(2))) =(√(3) √(2))^2+(√(3)+√(2))^2/(√(3) √(2))(√(3)+√(2)) 5 ...

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Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

If a=√3-√2√...

Question

If $a = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and $b = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , If the value of $a + b - 5 a b$ is $- 4 \sqrt{m} + 5$ then find $m$ .

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Solution

$a + b - 5 a b = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}} + \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} - 5 (\frac{(\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})}{(\sqrt{3} + \sqrt{2}) (\sqrt{3} - \sqrt{2})})$

$= \frac{(\sqrt{3} - \sqrt{2})^{2} + (\sqrt{3} + \sqrt{2})^{2}}{(\sqrt{3} - \sqrt{2}) (\sqrt{3} + \sqrt{2})} - 5 \times 1$

$= \frac{3 + 2 - 2 \sqrt{6} + 3 + 2 + 2 \sqrt{6}}{3 - 2} - 5$

$= \frac{10}{1} - 5 = 5 = - 4 \sqrt{m} + 5$

by comparing

$∴ m = 0$

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If a=√3−√2√3+√2 and b=√3+√2√3−√2, If the value of a+b−5ab is −4√m+5 then find m.

a+b−5ab=√3−√2√3+√2+√3+√2√3−√2−5((√3−√2)(√3+√2)(√3+√2)(√3−√2))=(√3−√2)2+(√3+√2)2(√3−√2)(√3+√2)−5×1=3+2−2√6+3+2+2√63−2−5=101−5=5=−4√m+5by comparing∴m=0

If $a = \frac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}$ and $b = \frac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}}$ , If the value of $a + b - 5 a b$ is $- 4 \sqrt{m} + 5$ then find $m$ .