9 grade maths> If a= 7+ 40 1/2 find x 1/2 +1/x 1/2

If a= 7+ 401/2 find x1/2 +1/x1/2

Rahul Jiji George , 10 Years ago

Grade 10

4 Answers

SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
Please find the answer to your question below
I assume that the value given as a be x
Then given x=7+ $\sqrt{40}$
it can also be written as x=( $\sqrt{2}$ + $\sqrt{5}$ )²
so we get $\sqrt{x}$ = $\sqrt{2}$ + $\sqrt{5}$
(1/ $\sqrt{x}$ )=1/( $\sqrt{5}$ + $\sqrt{2}$ )
by rationalising with $\sqrt{5}$ - $\sqrt{2}$ we get
(1/ $\sqrt{x}$ )=( $\sqrt{5}-\sqrt{2}$ )/3
Then $\sqrt{x}$ +( $1/\sqrt{x}$ )
=( $\sqrt{5}$ + $\sqrt{2}$ )+( $\sqrt{5}-\sqrt{2}$ )/3
=(4 $\sqrt{5}+2\sqrt{2}$ )/3

Rahul Jiji George

Last Activity: 10 Years ago

^{2 . can you please explain.}) $\sqrt{5}$ + $\sqrt{2}$ as x=( $\sqrt{40}$ sir,how did you get x=7+

Rahul Jiji George

Last Activity: 10 Years ago

sir, can you please explain how got as $\sqrt{40}$ x=7+²) $\sqrt{5}$ + $\sqrt{2}$ x=(

SHAIK AASIF AHAMED

Last Activity: 10 Years ago

Hello student,
Please find the clarification below
As we know that
(a+b)²=a²+2ab+b²
Similarly ( $\sqrt{a}$ + $\sqrt{b}$ )²=a+b+2 $\sqrt{a}$ $\sqrt{b}$ …..............(1)
given 7+ $\sqrt{40}$ =2+5+ $\sqrt{40}$
as $\sqrt{40}$ =2 $\sqrt{10}$ we get
7+ $\sqrt{40}$ =2+5+2 $\sqrt{10}$
=( $\sqrt{2}$ + $\sqrt{5}$ )²from property (1)
I hope its clear now