Question

please it is very urgent for me send photo​

Answer 1

$\Large{\underline{\underline{\mathfrak{\bf{Question}}}}}$

If ( x - 1/x ) = 3+2√2 , Find the value of 1/4(x³ - 1/x³)

$\Large{\underline{\underline{\mathfrak{\bf{Solution}}}}}$

$\Large{\underline{\mathfrak{\bf{\pink{Given}}}}}$

• ( x - 1/x ) = 3+2√2 .........(1)

$\Large{\underline{\mathfrak{\bf{\orange{Find}}}}}$

• Value of 1/4(x³ - 1/x³)

$\Large{\underline{\underline{\mathfrak{\bf{Explanation}}}}}$

We know,

★ ( a-b)² = a² + b² - 2ab

So,

★ ( x - 1/x )² = x² + 1/x² - 2.x.1/x

➥ (x - 1/x)² = x² + 1/x² - 2

Now, keep value by equ(1)

➥ (3+2√2)² = x²+1/x² - 2

➥3²+(2√2)²+2.3.2√2 = x²+1/x² - 2

➥ x² + 1/x² = (9+8+12√2)-2

➥ x² + 1/x² = 15 + 12√2

Again,

★(a³-b³) = (a-b)(a²+b²+ab)

So,

➥ (x³ - 1/x³ ) = (x - 1/x)(x² + 1/x² + x . 1/x)

➥(x³ - 1/x³ ) = (x - 1/x)(x² + 1/x² + 1)

keep value by equ(1) and (2)

➥ (x³ - 1/x³ ) = ( 3+2√2)(15+12√2+1)

➥ (x³ - 1/x³ ) = (3+2√2)(16+12√2)

➥ (x³ - 1/x³ ) = 4(3+2√2)(4+3√2)

➥ (x³ - 1/x³ ) = 4(12+9√2+8√2+12)

➥ (x³ - 1/x³ ) = 4(24+17√2)

Now, calculate ,

➥ 1/4 (x³ - 1/x³ ) = 4(24+17√2)/4

➥ 1/4 (x³ - 1/x³ ) = (24 + 17√2) (Ans.)

_____________________