Question

a और b का मान बताएं यदि 3+√7\3-√7=a+b√7​

Answer 1

Solution:-

Given

$\rm \: \implies \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} }$

To find

$\rm \implies \: a + b \sqrt{7}$

Now Take

$\rm \: \implies \: \dfrac{3 + \sqrt{7} }{3 - \sqrt{7} } \times \dfrac{3 + \sqrt{7} }{3 + \sqrt{7} }$

Using this identities

$\rm \to \: (a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab$

$\rm \to \: (a - b)(a + b) = {a}^{2} - {b}^{2}$

Now using this identities

$\rm \implies \: \dfrac{(3 + \sqrt{7} ) {}^{2} }{(3) {}^{2} - ( \sqrt{7}) {}^{2} }$

$\rm \implies \: \dfrac{3 {}^{2} + ( \sqrt{7} ) {}^{2} + 2 \times 3 \times \sqrt{7} }{(3) {}^{2} - ( \sqrt{7}) {}^{2} }$

$\rm \implies \dfrac{9 + 7 + 6 \sqrt{7} }{9 - 7}$

$\rm \implies \: \dfrac{16 + 6 \sqrt{7} }{2}$

$\rm \implies \: \dfrac{2(8 + 3 \sqrt{7} )}{2}$

$\rm \implies \: 8 + 3 \sqrt{7}$

So we get

$\rm \implies \: a = 8 \: \: and \: b = 3$

Answer 2

Answer:

a और b का मान है -

a= 8

b= 3

ऊपर दिए गए अटैचमेंट को देखें.