SOLUTION: I need help on these three questions: ~ 2a = 3b a^2 + b^2 = 117 ~ Find two numbers with a sum of 6 and with a quotient of -4. ~ A twenty-six meters of fencing is used to enc

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Question 1041248: I need help on these three questions:
~
2a = 3b
a^2 + b^2 = 117
~
Find two numbers with a sum of 6 and with a quotient of -4.
~
A twenty-six meters of fencing is used to enclose a rectangular lot with an area of 42 square meters. What are the dimensions of the lot?
I want to learn more about Quadratic Equations so I had these examples from the book. Please help for a test tomorrow!
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
I need help on these three questions:
~
2a = 3b
a^2 + b^2 = 117
~
Find two numbers with a sum of 6 and with a quotient of -4.
~
A twenty-six meters of fencing is used to enclose a rectangular lot with an area of 42 square meters. What are the dimensions of the lot?
I want to learn more about Quadratic Equations so I had these examples from the book. Please help for a test tomorrow!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

1.  2a = 3b,              (1)
    a%5E2+%2B+b%5E2 = 117.        (2)

    Multiply the eqn.(2) by 4 (both sides). You will get 

    4a%5E2+%2B+4b%5E2 = 4*117,   or

    %282a%29%5E2+%2B+4b%5E2 = 468.    (3)

    Now replace 2a in (3) by 3b, according to (1). You will get

    %283b%29%5E2+%2B+4b%5E2 = 468,   or  9b%5E2+%2B+4b%5E2 = 468,   or   13b%5E2 = 468.

    Now divide both sides by 13. You will get

    b%5E2 = 468%2F13 = 36.

    Hence, b = +/-sqrt%2836%29 = +/-6.

Answer.  b = 6,  a = 9   and/or   b = -6, a = -9.

Regarding your question #3, see the lesson
    - Problems on the area and the dimensions of a rectangle
in this site.

You will find there a lot of solved problems similar to yours.
Read them and consider them as the samples.
Then solve your problem on your own.

Also, look into this file  ALGEBRA-I - YOUR ONLINE TEXTBOOK.

It is your free online textbook in ALGEBRA-I.