Re: need help with 'if 1/a + 1/b = 3/8 and a*b = 3, then fin
Math wiz ya rite 09 said:
if 1/a + 1/b = 3/8 and a*b = 3,
then find a+b and a^2 + b^2
HELP??
1 / a + 1 / b = 3 / 8
Add the two fractions on the left-hand side. The common denominator is ab, right?
(b / ab) + (a / ab) = 3 / 8
(b + a) / (ab) = 3 / 8
Now, you are told that ab = 3. So,
(b + a) / 3 = 3 / 8
Multiply both sides by 3:
b + a = 9 / 8
There! You've got the value of a + b.
To find the value of a^2 + b^2, remember what happens when you SQUARE a binomial:
(a + b)<SUP>2</SUP> = a<SUP>2</SUP> + 2ab + b<SUP>2</SUP>
If you subtract 2ab from both sides of this, you'll have
(a + b)<SUP>2</SUP> - 2ab = a<SUP>2</SUP> + 2ab + b<SUP>2</SUP> - 2ab
or,
a<SUP>2</SUP> + b<SUP>2</SUP> = (a + b)<SUP>2</SUP> - 2ab
You know the value of (a + b), and you know the value of ab:
a<SUP>2</SUP> + b<SUP>2</SUP> = (9 / 8)<SUP>2</SUP> - 2(3)
You can do the arithmetic.....
