Question

x - (1/x) = 4 then x + (1/x) will be

Answer 1

given,

x-(1/x) = 4, find x+(1/x)

if we use, (a-b)² = a² -2ab + b² formula,

(x-(1/x)) = x² - 2(x)(1/x) + (1/x)²

substituting x-(1/x) for 4,

4² = x² - 2 + 1/x² (since x is being multiplied with 1/x and -2, we can cancel out both the x, and we get -2)

16 = x² + 1/x² - 2

16+2 = x² + 1/x²

18 = x² + 1/x²

now that we know, x² + 1/x² = 18, let us use the identity

(a+b)² = a² + 2ab + b²

(x+1/x)² = x² + 2(x)(1/x) + 1/x²

(again here x and 1/x gets cancelled)

(x+1/x)² = x² +1/x² + 2 (since it's addition we can rearrange the terms)

(x+1/x)² = 18+2 (as we before we found out x²+1/x² = 18)

(x+1/x)² = 20

(x+1/x) = √20

hope it helps