IF a - b=10 and a2 - b2=20, what is the value of b?

Answer 1

Correct answer is 10.

a-b=10 or 2a-2b=20 ...(1)
2a-2b=20 (Given)...(2)

Solving these,
4a=40
or a=10

Therfore, b=10.

Answer 2

A=30, B=20

Answer 3

B=10

a-b=10
20-10=10

a2-b2=20
20(2)-10(2)=20
40-20=20

Answer 4

10

Answer 5

b=20

Answer 6

b=-4

Factor the second equation into:
a^2-b^2=(a+b)(a-b)=20
divide each side by (a-b)
(a+b)(a-b)/(a-b) = 20/(a-b) = 20/10
a+b=2
Add b to both sides of the first equation:
a-b+b=a=10+b
Plug this value of a into the previous equation:
a+b=(10+b)+b=2
10+2b=2
2b+10-10=2-10
2b=-8
2b/2 = -8/2
b=-4
Solving for the value of a
a=10+b=10+(-4)=6

Checking if these values (a=6,b=-4) works:
6-(-4)=6+4=20
(6^2-(-4)^2)=36-16=20

I'm not 100% sure that there isn't a second solution, but b=-4 is certainly a correct value of b.

Answer 7

b = 0

Answer 8

If you mean a^2 - b^2 = 20, then

20 = a^2 - b^2 = (a+b)(a-b) = (a+b) x 10

So a-b = 10, a + b = 2

a = 6, b = -4

Answer 9

a-b = 10
a^2 - b^2 = 20

but a^2 - b^2 = (a-b)(a+b)
=> (a-b)(a+b) = 20
10(a+b) = 20
(a+b) = 2

a-b = 10
a+b = 2
add the two =>
2a = 12
a = 6

b = 2 - a = 2 - 6 = -4
or -b = 10 - a = 10 - 6 = 4 => b = -4

Answer 10

Erm if a^2-b^2 is 20 i.e.
(a-b)(a+b)=20
Since a-b=10
10(a+b)=20 Thus,
a+b=2 & a-b=10
Substitute for a=2-b thus,
2-b-b=10
2-2b=10
b=-4
But a+b=2
therefore a=6
a=6 and b=-4

Answer 11

a - b = 10
a^2 - b^2 = 20

a = b + 10

(b + 10)^2 - b^2 = 20
((b + 10)(b + 10)) - b^2 = 20
b^2 + 10b + 10b + 100 - b^2 = 20
20b + 100 = 20
20b = -80
b = -4

a = b + 10
a = -4 + 10
a = 6

6^2 - (-4)^2 = 20
36 - 16 = 20
20 = 20

ANS : b = -4