Question

If x = 2/(3 +√7 ) , then (x-3)^2 is

Answer 1

Answer:

7 is the value

Step-by-step explanation:

$x = \frac{2}{3 + \sqrt{7} }$

Now we need to rationalise the following value to make it easier to solve,

$x = \frac{2}{3 + \sqrt{7} } \times \frac{3 - \sqrt{7} }{3 - \sqrt{7} }$

In the denominator we can use the identity which says :

$(x + y)(x - y) = x ^{2} - {y}^{2}$

$x = \frac{6 - 2 \sqrt{7} }{(3) ^{2} - ( \sqrt{7}) ^{2} }$

$x = \frac{6 - 2 \sqrt{7} }{9 - 7}$

$x = \frac{6 - 2 \sqrt{7} }{2}$

$x = 3 - \sqrt{7}$

Now we have to find the value of (x-3) and square the following,

$(x - 3) = 3 - \sqrt{7} - 3$

$(x - 3) = - \sqrt{7}$

Now squaring this value we get:

$(x - 3) ^{2} = ( - \sqrt{7} ) ^{2}$

$(x - 3)^{2} = 7$

Answer 2

Answer:

7

Step-by-step explanation:

100% answer 7