Question

$ifx = 1 \div 3 - \sqrt{8 \: \: } find \: the \: value \: of \: {x}^{3} - 2 {x}^{2} - 7x + 5$


Explain this method done in given picture (of RS aggraval class 9)

Answer 1

heya...!!!!


given that:-

x = 1/(3 - √8)

now rationalize the denominator

$x = \frac{1}{3 - \sqrt{8} } \times \frac{3 + \sqrt{8} }{3 + \sqrt{8} } \\ \\ = > \frac{3 + \sqrt{8} }{ {3}^{2} - { \sqrt{8} }^{2} } \: \: \: using \: (a - b)(a + b) = {a}^{2} - {b}^{2} \\ \\ = > \frac{3 + \sqrt{8} }{9 - 8} \\ \\ = > 3 + \sqrt{8}$
x = (3 + √8)

on squaring both side

we get,

x² = 3² + √8² + 2×3×√8

=> x² = 9 + 8 + 6√8

=> x² = (17 + 6√8)


now,

x³ - 2x²- 7x + 5

=> x(x² - 2x - 7) + 5

=> (3 + √8)(17 + 6√8 - 2(3 + √8) - 7) + 5

=> (3 + √8)(17 + 6√8 - 6 - 2√8 - 7) + 5

=> (3 + √8)(4 + 4√8) + 5

=> (12 + 12√8 + 4√8 + 32) + 5

=> (44 + 16√8) + 5

=> 49 + 16√8

=> 49 + 16×2√2 [ √8 = √(2×2×2) = 2√2 ]

=> 49 + 32√2