If x+1/x=7 then x^2-1/x^2=
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Answer:
21√5
Step-by-step explanation:
Given, x+1/x=7
we know (a - b)^2 = (a + b)^2 - 4ab
If we take a= x & b= 1/x then
(x - 1/x)^2 = ( x + 1/x )^2 - 4× x × 1/x
by putting the value x+1/x=7
(x - 1/x)^2 = 7^2 - 4 = 49 - 4 = 45
(x - 1/x) = √45 = √9×5 = 3√5
now by formula a^2 - b^2 = (a+b)(a-b)
x^2-1/x^2 = (x+1/x)(x-1/x)
x^2-1/x^2 = 7 × 3√5 = 21√5
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