X+1/x is given find x-1/x and x^5-1/x^5 | SSC | Maths Concept | Maths Magic
Автор: JAI MATHS CLASSES
Загружено: 2026-02-22
Просмотров: 9
Описание:
When you are given x - \frac{1}{x} = 3, you are essentially being given a shortcut to find any power of x by manipulating these formulas:
Square Identity: (a \pm b)^2 = a^2 + b^2 \pm 2ab
Cube Identity: (a \pm b)^3 = a^3 \pm b^3 \pm 3ab(a \pm b)
Finding the Square (x^2 + \frac{1}{x^2})
To find the value of x^2 + \frac{1}{x^2}, we take your given equation and square both sides:
(x - \frac{1}{x})^2 = 3^2
Using the identity (a - b)^2 = a^2 - 2ab + b^2:
Because x and \frac{1}{x} cancel out, the equation becomes:
Because x and \frac{1}{x} cancel out, the equation becomes:
Notice that we can substitute the original value (x - \frac{1}{x} = 3) back into the equation:
#ctet #maths #mathtricks #exam #exam #mathstricks
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