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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

Grade:10

4 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 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
42 Points
9 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
42 Points
9 years ago
sir,   can you please explain how got as\sqrt{40} x=7+2)\sqrt{5}+\sqrt{2} x=(
 
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
9 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

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