Question

7+3✓5/3+✓5-7-3✓5/3-✓5=a+✓5b find the value of a and b

Answer 1

answer is 36÷77×457+567=4680

Answer 2

Answer:

⇒ a = 0 and b = 1

Step-by-step explanation:

We have ,

$= > \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } - \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} }$

$= > ( \frac{7 + 3 \sqrt{5} }{3 + \sqrt{5} } \times \frac{3 - \sqrt{5} }{3 - \sqrt{5} } ) - ( \frac{7 - 3 \sqrt{5} }{3 - \sqrt{5} } \times \frac{3 + \sqrt{5} }{3 + \sqrt{5} } )$

$= > \frac{(21 + 7 \sqrt{5} + 9 \sqrt{5} - 15)}{(3 + \sqrt{5})(3 - \sqrt{5} ) } - \frac{(21 + 7 \sqrt{5} - 9 \sqrt{5} - 15)}{(3 - \sqrt{5} )(3 + \sqrt{5} )}$

$= > \frac{(6 + 2 \sqrt{5} )}{(3) ^{2} - ( \sqrt{5})^{2} } - \frac{(6 - 2 \sqrt{5}) }{(3)^{2} - ( \sqrt{5}) ^{2} }$

$= > \frac{(6 + 2 \sqrt{5} )}{(3) ^{2} - ( \sqrt{5})^{2} } - \frac{(6 - 2 \sqrt{5}) }{(3)^{2} - ( \sqrt{5}) ^{2} }$

$= > \frac{(6 + 2 \sqrt{5} )}{(9 - 5)} - \frac{(6 - 2 \sqrt{5} )}{(9 - 5)}$

$= > \frac{6 + 2 \sqrt{5} }{4} - \frac{6 - 2 \sqrt{5} }{4}$

$= > \frac{6 + 2 \sqrt{5} - 6 - 2 \sqrt{5} }{4}$

$= > \frac{4 \sqrt{5} }{4} = \sqrt{5}$

∴ 7 + 3√5 / 3 + √5 - 7 - 3√5 /3 - √5 = a + √5 b

Comparing on both the sides , we get ;

⇒ √5 = a + √5 b

⇒ a = 0 and b = 1