If a+b=1 and a−b=7 ;
Find
(i) (a2+b2) (ii) ab
3
(i) Given that a + b = 1 and (a- b) = 7
Squaring (a+b) , we get
(a+b)2 = a2+2ab+b2
(1)2 = a2+2ab+b2
1=(a2+2ab+b2) ----------------------------(1)
Similarly Squaring (a-b) , we get
(a−b)2 = a2−2ab+b2
(7)2 = a2−2ab+b2
49=(a2−2ab+b2) ----------------------------------(2)
Adding (1) and (2) , we get
1=(a2+2ab+b2)
+ 49=(a2−2ab+b2)
____________________________
50=2(a2+b2)
25=(a2+b2)
(ii) We know 25=(a2+b2)
Substituting in 1st equation , we get
1=(25+2ab)
−24=2ab
ab=−12