Question

9. If a - b = 4 and a + b = 6: find(i) a^2+b^2
(ii) ab​

Answer 1

a - b = 4

a + b = 6

1. Find $a^{2} + b^{2}$ and ab.

FORMULAS WE ARE GONNA USE

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

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

In eq 1

(6)^2 = a2 + b2 + 2ab

36 - 2ab = a2 + b2

Substituting value of a2+b2 in equation number 2.

4^2 = 36 - 2ab - 2ab

16 - 36 = -4ab

-16 = -4ab

ab = 4

a2 + b2 = 36 - 4 x 2 = 36 - 8 = 28

Answer 2

step 1: a-b = 4

therefore a=4+b

step 2: using a in second equation in place of a we get : 4+b + b = 6

therefore 2b = 6-4

therefore b = 2/2

b = 1

step 3: using b in first equation in place of b we get: a-1 = 4

therefore a=5

step 5: a² + b² = (5²) + (1²) + 2(5)(1)

= 25 + 1 + 10

= 36 ans

step 6: ab = 5 * 1

= 5 ans