If a - b = 4 and a + b = 6; find : (i) a 2 + b 2 (ii) ab

(i) We know that, (a - b) 2 = a 2 + b 2 - 2ab .............(1) (a + b) 2 = a 2 + b 2 + 2ab ..............(2) Adding equation (1) and (2), we get : (a - b) 2 + (a + b) 2 = 2(a 2 + b 2 ) (a 2 + b 2 ) = Substituting values we get : Hence, a 2 + b 2 = 26. (ii) We know that, (a - b) 2 = a 2 + b 2 - 2ab .............(1) (a + b) 2 = a 2 + b 2 + 2ab ..............(2) Subtracting equation (1) from (2), we get : ⇒ (a + b) 2 - (a - b) 2 = a 2 + b 2 + 2ab - (a 2 + b 2 - 2ab) ⇒ (a + b) 2 - (a - b) 2 = 4ab ⇒ ab = Substituting values we get : Hence, ab = 5.

Mathematics

If a - b = 4 and a + b = 6; find :
(i) a² + b²
(ii) ab

Expansions

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Mathematics

If a - b = 4 and a + b = 6; find :
(i) a² + b²
(ii) ab

Expansions

Related Questions

If a - b = 0.9 and ab = 0.36; find :
(i) a + b
(ii) a² - b²

Mathematics

If a - b = 4 and a + b = 6; find :(i) a2 + b2(ii) ab

Expansions

Related Questions

If a - b = 0.9 and ab = 0.36; find :(i) a + b(ii) a2 - b2

If a - b = 4 and a + b = 6; find :
(i) a² + b²
(ii) ab

If a - b = 0.9 and ab = 0.36; find :
(i) a + b
(ii) a² - b²