Question

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If x = 1 - 2 - √3 , then find the value of x³- 2x² - 7x + 5

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Answer 1

Solution:-

Given that

x = 1 - 2 - √3

x = - 1 - √3

We have to find the value of

x³ - 2x² - 7x + 5

Putting the value of x

(- 1 - √3)³ - 2(- 1 - √3)² - 7(- 1 - √3) + 5

Using (a - b)³ = a³ - 3a²b + 3ab² - b³ to expand the expression.

= - 1 - 3√3 - 9 - 3√3 - 2(- 1 - √3)² - 7(- 1 - √3) + 5

Factorising the negative sign from the expression.

= - 1 - 3√3 - 9 - 3√3 - 2(- (1 + √3))² - 7(- 1 - √3) + 5

Distribute - 7 through the parentheses.

= - 1 - 3√3 - 9 - 3√3 - 2(- (1 + √3))² + 7 + 7√3 + 5

A negative base raised to an even power equals a positive.

= - 1 - 3√3 - 9 - 3√3 - 2(1 + √3)² + 7 + 7√3 + 5

Use (a + b)² = a² + 2ab + b² to expand the expression.

= - 1 - 3√3 - 9 - 3√3 - 2(1 + 2√3 + 3) + 7 + 7√3 + 5

Add the numbers.

= - 1 - 3√3 - 9 - 3√3 - 2(4 + 2√3) + 7 + 7√3 + 5

Distribute - 2 through the parentheses.

= - 1 - 3√3 - 9 - 3√3 - 8 - 4√3 + 7 + 7√3 + 5

Calculate the sum and difference.

= - 6 - 3√3 - 3√3 - 4√3 + 7√3

Grouping the like terms.

= - 6 - 3√3

Answer 2

Anita hassanadani bhi hai cast mai

aur mere questions dekh kuch blank hai inke answers dedo please