Question

If a^2+b^2=34 and ab=15 find the value of a+b and a-b

Answer 1

Answer:

a+b =+8 or -8

a-2b =+2 or -2

Step-by-step explanation:

a^2+b^2=34

ab=15

(a+b)^2=a^2+b^2+2ab

(a+b)^2=34+2×15

( a+b)^2=64

a+b=√64

a+b=+8 or -8

(a-b)^2=a^2+b^2-2ab

(a - b)^2=34-2×15

(a - b)^2=34-30

(a - b)^2=4

a - b=√4

a - b=+2or-2

Answer 2

Answer:

a + b = 8

and

a - b = 2

Step-by-step explanation:

given,

a^2 + b^2 = 34 and ab = 15 therefore 2ab = 30

1)we can added 2ab in equation on both sides

we get,

a^2 + b^2 + 2ab = 34 + 2ab

we know that a^2 + b^2 + 2ab = (a +b)^2

therefore (a+b)^2 = 34+30

(a+b)^2 = 64

take the square root on both sides we get

a + b = 8

2) we can subtract 2ab in equation on both side we get

a^2 + b^2 -2ab = 34 - 2ab

(a-b)^2 = 4

therefore a-b = 2