Question

Plese find the (iii) Bit From Selina Class 9 Chapterwise revision​

Answer 1

Solution

Given :

• x² + 1/x² = 7_________(1)

Find :-

• Value of (1) x - 1/x ,
• (2) x + 1/x
• (3). 3x² - 3/x²

Explantion

We Know,

★ ( x + 1/x)² = x² + 2.x.1/x + 1/x² = x² + 1/x² + 2

First we calculate, ( x + 1/x).

we Have,

==> (x + 1/x)² = x² + 1/x² + 2

keep value by equ(1) .

==> (x + 1/x)² = 7 + 2

==> (x + 1/x)² = 9

==> (x + 1/x )² = 3²

==> x + 1/x = 3 [ Ans ].__________(2)

_________________________

Now, calculate , ( x - 1/x).

==> (x - 1/x)² = x² + 1/x² - 2

keep value by equ(1)

==> (x - 1/x)² = 7 - 2

==> (x - 1/x)² = 5

==> (x - 1/x) = √5. [ Ans].__________(3)

________________________

Now, Calculate (3x² - 3/x²)

For this,

Multiply by equ(2) & equ(3)

==> (x + 1/x)(x - 1/x) = 3×√5

==> x² - 1/x² = 3√5 ________________(4)

Now, Multiply by 3 both side in equ(4)

==> 3(x² - 1/x²) = 3 × 3√5

==> 3(x² - 1/x)² = 9√5. [ Ans]

_____________________

Answer 2

Step-by-step explanation:

☞︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎Fᴏʀ ǫᴜᴇsᴛɪᴏɴ (1)

✫Find :-

• x-1/x

✫Given:-

• x^2 + 1/x^2 =7

✫Formula:-

$\tt ({x - \frac{1}{x} )}^{2} = {x}^{2} - 2 \times x \times \frac{1}{x} + {( \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2$

✫Now put the values in formula,

$\tt ({x - \frac{1}{x} )}^{2} = 7 - 2 \\ \tt\tt ({x - \frac{1}{x} )}^{2} = 5 \\ \tt x - \frac{1}{x} = \sqrt{5}$

︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎☞︎︎︎Fᴏʀ ǫᴜᴇsᴛɪᴏɴ (2)

✫Find:-

•x + 1/x

✫Given:-

•x^2 + 1/x^2 =7

✫Formula:-

$\tt ({x + \frac{1}{x} )}^{2} = {x}^{2} + 2 \times x \times \frac{1}{x} + {( \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2$

✫Now put the values in formula,

$\tt ({x + \frac{1}{x} )}^{2} = 7 + 2 \\ \tt\tt ({x + \frac{1}{x} )}^{2} = 9\\ \tt x + \frac{1}{x} = \sqrt{9} = 3$

︎︎︎︎︎︎︎︎︎︎︎︎︎︎︎☞︎︎︎Fᴏʀ ǫᴜᴇsᴛɪᴏɴ (3)

✫Find:-

•3x^2 - 3/x^2 or 3(x^2 - 1/x^2)

✫Given:-

•x^2 + 1/x^2 =7

✫Formula:-

$</p><p>\tt ({x - \frac{1}{x} )}^{2} = {x}^{2} - 2 \times x \times \frac{1}{x} + {( \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2$

✫Now put the values in formula,

$\tt ({x - \frac{1}{x} )}^{2} = 7 - 2 \\ \tt\tt ({x - \frac{1}{x} )}^{2} = 5 \\ \tt x - \frac{1}{x} = \sqrt{5}$

✫Now multiply 3 on both sides,

$\tt3( {x}^{2} - \frac{1}{ {x}^{2} }) = 3 \times \sqrt{5} \\ \tt3 {x}^{2} - \frac{3}{ {x}^{2} } = 3 \sqrt{5}$

___________________________

Thanks for question