If p - q = 9 and pq = 36, evaluate (i) p + q (ii) p 2 - q 2 .

(i) We know that, (p - q) 2 = p 2 + q 2 - 2pq ⇒ (p - q) 2 = p 2 + q 2 + 2pq - 2pq - 2pq ⇒ (p - q) 2 = (p + q) 2 - 4pq ⇒ (p + q) 2 = (p - q) 2 + 4pq ⇒ (p + q) = Substituting value we get, Hence, p + q = ±15. (ii) p 2 - q 2 = (p - q)(p + q). Substituting value we get, ⇒ p 2 - q 2 = 9 × ±15 = ±135. Hence, p 2 - q 2 = ±135.

If a² + b² = 13 and ab = 6, find
(i) a + b
(ii) a - b

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If a + b = 4 and ab = -12, find
(i) a - b
(ii) a² - b².

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If x + y = 6 and x - y = 4, find
(i) x² + y²
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Mathematics

If p - q = 9 and pq = 36, evaluate
(i) p + q
(ii) p² - q².

Expansions

Related Questions

If a² + b² = 13 and ab = 6, find
(i) a + b
(ii) a - b

If a + b = 4 and ab = -12, find
(i) a - b
(ii) a² - b².

If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy.

Mathematics

If p - q = 9 and pq = 36, evaluate(i) p + q(ii) p2 - q2.

Expansions

Related Questions

If a2 + b2 = 13 and ab = 6, find(i) a + b(ii) a - b

If a + b = 4 and ab = -12, find(i) a - b(ii) a2 - b2.

If x + y = 6 and x - y = 4, find(i) x2 + y2(ii) xy.

If p - q = 9 and pq = 36, evaluate
(i) p + q
(ii) p² - q².

If a² + b² = 13 and ab = 6, find
(i) a + b
(ii) a - b

If a + b = 4 and ab = -12, find
(i) a - b
(ii) a² - b².

If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy.