Math, asked by goma174, 9 months ago

If x+1/x=7 then x^2-1/x^2=​

Answers

Answered by harshittiwari92
2

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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