If a-5-3-5-3 and b-5-3-5-3 Find a2-b2-6ab

a=√(5) √(3)√(5)+√(3)×√(5) √(3)√(5) √(3)=5+3 2√(15)5 3=8 2√(15)2=4 √(15) b=√(5)+√(3)√(5) √(3)×√(5)+√(3)√(5)+√(3)=5+3+2√(15)5 3=8+2√(15)2=4+√(15) a ...

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Byju's Answer

Standard IX

Mathematics

Expansion of (a ± b ± c)²

If a=√5-√3√...

Question

If $a = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ and $b = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$
Find $a^{2} + b^{2} - 6 a b$

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Solution

$a = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}} \times \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \frac{5 + 3 - 2 \sqrt{15}}{5 - 3} = \frac{8 - 2 \sqrt{15}}{2} = 4 - \sqrt{15}$
$b = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}} \times \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} + \sqrt{3}} = \frac{5 + 3 + 2 \sqrt{15}}{5 - 3} = \frac{8 + 2 \sqrt{15}}{2} = 4 + \sqrt{15}$
$a^{2} + b^{2} - 6 a b$
$= a^{2} + b^{2} - 2 a b - 4 a b$
$= {(a - b)}^{2} - 4 a b$
$= {(4 - \sqrt{15} - 4 - \sqrt{15})}^{2} - 4 (4 - \sqrt{15}) (4 + \sqrt{15})$
$= 4 \times 15 - 4 (16 - 15)$
$= 60 - 4 = 56$

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If a=√5−√3√5+√3 and b=√5+√3√5−√3 Find a2+b2−6ab

a=√5−√3√5+√3×√5−√3√5−√3=5+3−2√155−3=8−2√152=4−√15b=√5+√3√5−√3×√5+√3√5+√3=5+3+2√155−3=8+2√152=4+√15a2+b2−6ab=a2+b2−2ab−4ab=(a−b)2−4ab=(4−√15−4−√15)2−4(4−√15)(4+√15)=4×15−4(16−15)=60−4=56

If $a = \frac{\sqrt{5} - \sqrt{3}}{\sqrt{5} + \sqrt{3}}$ and $b = \frac{\sqrt{5} + \sqrt{3}}{\sqrt{5} - \sqrt{3}}$
Find $a^{2} + b^{2} - 6 a b$