Question

It x=9-4√5, find the value of 1/5​

Answer 1

Step-by-step explanation:

Value of 1/5 will always be 0.2, whether the equations are given or not.

If the question is " find the value of 1/x, then..

$\frac{1}{x} = \frac{1}{9 - 4 \sqrt{5} }$

Now, multiplying by conjugate of denominator (i.e. 9 + 4√5 ) in numerator and denominator

$\frac{1 \times (9 + 4 \sqrt{5)} }{(9 - 4 \sqrt{5} ) \times (9 + 4 \sqrt{5)} }$

$\frac{9 + 4 \sqrt{5} }{ {9}^{2} - {(4 \sqrt{5} )}^{2} } \\ = \frac{9 + 4 \sqrt{5} }{81 - 80} \\ = 9 + 4 \sqrt{5}$

Hence, the value of 1/x = (9 + 4√5).