SOLUTION: Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers

Question 1037851: Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers

Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

So as we see, the two equations are equivalent. So there was no need for both those equivalent equations to have been given. Just one of them was all that was necessary. So we just solve for one of the variables in terms of the other: That's a quadratic in two variables. It is symmetrical in a and b. Solving for a in terms of b. To avoid a conflict of letters, we CAPITALIZE the letters of the quadratic formula Now we want to find We rationalize the denominator: 3b � 2√2b + b �� = 3b � 2√2b - b 4b � 2√2b �� = 2b � 2√2b 2 � √2 �� = 1 � √2 (2 � √2)(1 ∓ √2) �� = (1 � √2)(1 ∓ √2) 2 � √2 ∓ √2 - 2 �� = 1 � √2 ∓ √2 - 2 ∓√2 �� = -1 �√2 Edwin

Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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Find the value of (a+b)/(a-b) if (a+b)^2 = 8ab and a^2 + b^2 = 6ab. a and b are real numbers
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There is much shorter and much straightforward solution.

Instead of , let us consider the square of this expression, . It is = ( <--- I replaced in the numerator by 8ab according to the condition ) = = ( <--- I replaced in the denominator by 6ab according to the condition ) = = 2. Since the square of the expression is equal to 2, the expression itself is +/-: = +/-.

There is no need to solve any equations.

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