Question

if √2+√7/√2-√7=a+b√14,find a,b​

Answer 1

Answer:

-9/5 -2/5√14 =a+b √14

a= -9/5,b= -2/5

Answer 2

The value of $a \: and \: b \: are \: \frac{ - 9}{5} \: and \: \frac{ - 2 }{5} respectively$

Given:

√2+√7/√2-√7=a+b√14

To Find:

a and b.

Solution:

To find the value of a and b we will follow the following steps:

As we know,

$\frac{ \sqrt{2} + \sqrt{7} }{ \sqrt{2} - \sqrt{7} } = a + b \sqrt{14}$

Multiplying the denominator and numerator of the left-hand side by the same numerator we get,

$\frac{ \sqrt{2} + \sqrt{7} \times \sqrt{2} + \sqrt{7}}{ \sqrt{2} - \sqrt{7} \times \sqrt{2} + \sqrt{7}} = a + b \sqrt{14}$

$\frac{ { (\sqrt{2 } + \sqrt{7} )}^{2} }{ { \sqrt{2} }^{2} - { \sqrt{7} }^{2} } = a + b \sqrt{14}$

$\frac{2 + 2 \sqrt{2} \sqrt{7} + 7}{2 - 7} = a + b \sqrt{14}$

$\frac{9 + 2 \sqrt{14} }{ - 5} = a +b \sqrt{14}$

$\frac{ - 9}{5} + \frac{ - 2 \sqrt{14} }{5} = a +b \sqrt{14}$

On comparing both sides we get,

$a \: and \: b \: are \: \frac{ - 9}{5} \: and \: \frac{ - 2 }{5} respectively$

Henceforth, the value of $a \: and \: b \: are \: \frac{ - 9}{5} \: and \: \frac{ - 2 }{5} respectively$

#SPJ3