If x + y = 6 and x – y = 4, find

If x + y = 6 and x – y = 4, find

(i) x² + y²

(ii) xy

Answer :

We know that

(x + y)² – (x – y)² = 4xy

Substituting the values

6² – 4² = 4xy

By further calculation

36 – 16 = 4xy

20 = 4xy

4xy = 20

So we get

xy = 20/4 = 5

(i) x² + y² = (x + y)² – 2xy

Substituting the values

= 6² – 2 × 5

By further calculation

= 36 – 10

= 26

(ii) xy = 5

More Solutions:

• Prove that x2 + 1/x2 = x3 + 1/x3 = x4 + 1/x4.
• If x – 2/x = 3, find the value of x3 – 8/x3.
• If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.
• If a + 1/a = p, prove that a3 + 1/a3 = p (p2 – 3).
• If x2 + 1/x2 = 27, find the value of x – 1/x.
• Find the value of 3×3 + 5x – 3/x3 – 5/x.
• If x2 + 1/25×2 = 8 3/5, find x + 1/5x.
• If x2 + 1/4×2 = 8, find x3 + 1/8×3.
• If a2 – 3a + 1 = 0, find
• If a = 1/ (a – 5), find