Question

Kindly answer it fast​

Answer 1

Answer:

17) x² + 1/x² = 27

18) Quotient = (2x - 5)

     Remainder = 0

Step-by-step explanation:

Question - 17 :

Given,

• x - 1/x = 5

To find,

• the value of x² + 1/x²

Solution,

  we know,

 (a - b)² = a² + b² - 2ab

Substituting a = x and b = 1/x ,

  $\sf (x-\dfrac{1}{x})^2=x^2+(\dfrac{1}{x})^2-2(x)(\dfrac{1}{x}) \\\\ (x-\dfrac{1}{x})^2=x^2+\dfrac{1}{x^2} - 2 \\\\ 5^2=x^2+\dfrac{1}{x^2}-2 \\\\ 25=x^2+\dfrac{1}{x^2} -2 \\\\ x^2+\dfrac{1}{x^2}=25+2 \\\\ x^2+\dfrac{1}{x^2}=27$

The value of (x² + 1/x² ) is 27

Question - 18 :

  we have to find the quotient and remainder when (14x² - 53x + 45) is divided by (7x - 9)

Dividend = 14x² - 53x + 45

Divisor = (7x - 9)

By long division method,

   $\sf \large \begin{array}{c|c|c}\sf 7x-9&\sf 14x^2-53x+45 & \sf 2x-5 \\&\sf 14x^2-18x \qquad \ \\ & - \quad + \ \ \ \ \ \qquad & \\ \cline{2-2} & \sf 0-35x+45 \\ &\sf \ \ \ -35x+45 \\ & + \quad - \\ \cline{2-2} & \sf \ 0 \end{array}$

Remainder = 0

Quotient = (2x - 5)

Verification :

 Dividend = [Divisor × Quotient] + Remainder

14x² - 53x + 45 = [(7x - 9) × (2x - 5)] + 0

14x² - 53x + 45 = 7x(2x - 5) - 9(2x - 5)

14x² - 53x + 45 = 14x² - 35x - 18x + 45

14x² - 53x + 45 = 14x² - 53x + 45

LHS = RHS

Hence verified!