Question

If a + b = 1 and a - b = 7 ; Find

(i) $(a^2+b^2)$ (ii) ab

• A. (i) 25 (ii) -12
• B. (i) 51 (ii) 12
• C. (i) 26 (ii) -13
• D. (i) -25 (ii) 12

Answer 1

The correct option is A

(i) 25 (ii) -12

(i) Given that a + b = 1 and (a- b) = 7

Squaring (a+b) , we get

$(a+b{)}^2$ = $a^2+2ab+b^2$
$(1{)}^2$ = $a^2+2ab+b^2$
$1=(a^2+2ab+b^2$) ----------------------------(1)

Similarly Squaring (a-b) , we get
$(a-b{)}^2$ = $a^2-2ab+b^2$
$(7{)}^2$ = $a^2-2ab+b^2$
$49=(a^2-2ab+b^2$) ----------------------------------(2)

Adding (1) and (2) , we get

$1=(a^2+2ab+b^2$)
+ $49=(a^2-2ab+b^2$)
____________________________
$50=2(a^2+b^2$)
$25=(a^2+b^2$)

(ii) We know $25=(a^2+b^2$)

Substituting in 1st equation , we get

$1=(25+2ab$)
- 24 = 2ab
ab = - 12