Question 1209081: One ordered pair (a,b) satisfies the two equations ab^4 = 48 and a^2 b^3 = 24/b^5. What is the value of b in this ordered pair? (Note: you may have to use the Tab key to get your cursor into the middle answer box.)
Answer by ikleyn(52784)   (Show Source):
You can put this solution on YOUR website! .
One ordered pair (a,b) satisfies the two equations ab^4 = 48 and a^2*b^3 = 24/b^5.
What is the value of b in this ordered pair?
(Note: you may have to use the Tab key to get your cursor into the middle answer box.)
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Second equation is
a^2*b^3 =  ,
which is equivalent to
a^2*b^8 = 24. (1)
Compare it with the first equation
ab^4 = 48. (2)
Left side of (1) is the square of the left side of (2),
but right side of (1) is NOT the square of the right side of (2).
This contradiction shows and proves that the situation, described in the post,
NEVER may happen and, consequently, such ordered pair (a,b) DOES NOT exist.
Solved, with complete explanations.
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