Question

Find the value of (x^2+1/x^2),if (x-1/x)=7

Answer 1

Answer:

x²+1/x² = 51

Step-by-step explanation:

x²+1/x² = 51

Given x - 1/x = 7 ---(1)

We know the algebraic identity:

a²+b²-2ab = (a-b)²

Or

a²+b² = (a-b)²+2ab

Now,

x²+1/x²

= (x-1/x)²+2*x*(1/x)

= (x-1/x)²+2

= 7²+2 [ from (1)]

= 49+2

= 51

Therefore,

x²+1/x² = 51

Hope this helps....

Answer 2

Given :-

• x - 1/x = 7

To find :-

• x² + 1/x²

Solution :-

• x - 1/x = 7

Squaring both side

→ (x - 1/x)² = (7)²

Apply identity : (a - b)² = a² + b² - 2ab

→ x² + 1/x² - 2 × x × 1/x = 49

→ x² + 1/x² - 2 = 49

→ x² + 1/x² = 49 + 2

→ x² + 1/x² = 51

Extra Information

• (a + b)² = a² + b² + 2ab
• a² - b² = (a + b)(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)