Question 1209561: If 7^sin²x - 7^cos²x = 8
find the value of x.
Answer by ikleyn(53763)   (Show Source):
You can put this solution on YOUR website! .
If 7^sin²x - 7^cos²x = 8
find the value of x.
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The starting equation is
7^(sin^2(x)) - 7^(cos^2(x)) = 8.
Due to OBVIOUS reasons, this equation has no real solutions.
Indeed, sin^2(x) has the maximum value of 1; hence, 7^(sin^2(x)) has maximum value of 7.
Next, from 7^(sin^2(x)), the equation subtracts 7^(cos^2(x)), which is non-negative
real number, so the left side of the equation CAN NOT be greater than 7.
A fortiori, it can not be 8.
At this point, my solution is complete, and the
ANSWER is: this given equation has no solution/solutions in real numbers.
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