Question

Question :-
If x + 1/x = 3 then find x² + 1/x²

Answer 1

Given :-

$\sf \bullet \;\; x + \dfrac{1}{x} = 3$

To Find :-

$\sf \bullet \;\; x^{2} + \dfrac{1}{x^{2}}$

Solution :-  

$\sf : \; \implies x + \dfrac{1}{x} = 3$

$\bf \; \bigg\{ \; Squaring\;both\;sides \; \bigg\}$

$\sf : \; \implies \{ \; 3 \; \}^{2} = \bigg\{ x + \dfrac{1}{x} \bigg\}^{2}$

$\bf \; \bigg\{ \; ( a + b )^{2} = a^{2} + b^{2} + 2ab \; \bigg\}$

$\sf : \; \implies 9 = x^{2} + \dfrac{1}{x^{2}} + 2 \times x \times \dfrac{1}{x}$

$\sf : \; \implies 9 = x^{2} + \dfrac{1}{x^{2}} + 2 \times 1$

$\sf : \; \implies 9 = x^{2} + \dfrac{1}{x^{2}} + 2$

$\sf : \; \implies x^{2} +\dfrac{1}{x^{2}} = 9 -2$

$\boxed{\bf{ \bigstar \;\; x^{2} + \dfrac{1}{x^{2}} = 7 }}$

•  Henceforth, the value of x² + 1/x²  is 7

Answer 2

Answer:

Hence, the value of x^2 + 1/x^2 is 7.

Step-by-step explanation:

Given:-

x + 1/x = 3

To find out:-

Value of x^2 + 1/x^2

Solution:-

We have

x + 1/x = 3

Now, squaring on both sides, we get

(x + 1/x)^2 = (3)^2

Now, applying algebraic Identity because our expression in the form of:

(a + b)^2 = a^2 + 2ab + b^2

Where, we have to put in our expression a = x and b = 1/x , we get

→ x^2 + 2(x)(1/x) + (1/x)^2 = 9

→ x^2 + 2 + (1/x)^2 = 9

→ x^2 + 2 + 1/x^2 = 9

→ x^2 + 1/x^2 = 9 - 2

→ x^2 + 1/x^2 = 7

Answer:-

Hence, the value of x^2 + 1/x^2 is 7.

Used formulae:-

(a + b)^2 = a^2 + 2ab + b^2