Question

sixth sum both parts​

Answer 1

Answer:

(a) 11

(b) 119

Step-by-step explanation:

⇒ (a)

• Square both sides of 'x + 1/x = 3'. According to (a - b)² = a² - 2ab + b², the LHS becomes x² - 2 + 1/x² = 9.
• Add 2 to both sides to get the answer 11.

⇒ (b)

• Square both sides of 'x² + 1/x² = 11'. According to (a + b)² = a² + 2ab + b², the LHS becomes x⁴ + 2 + 1/x⁴ = 121.
• Subtract 2 from both sides to get the answer 119.

Method:

⇒ (a)

$\bullet\ (x-\frac{1}{x})^2=3^2 \\ \\ \bullet\ x^2-2 \times x \times \frac{1}{x}+\frac{1}{x^2}=9 \\ \\ \bullet\ x^2+\frac{1}{x^2}-2=9 \\ \\ \bullet\ x^2+\frac{1}{x^2}=\bold{11}$

⇒ (b)

$\bullet\ (x^2+\frac{1}{x^2})^2=11^2 \\ \\ \bullet\ x^4+2 \times x^2 \times \frac{1}{x^2}+\frac{1}{x^4}=121 \\ \\ \bullet\ x^4+\frac{1}{x^4}+2=121 \\ \\ \bullet\ x^2+\frac{1}{x^2}=\bold{119}$