Asked by christian
What values of c and d make the equation true? Assume x greater-than 0 and y greater-than-or-equal-to 0
StartRoot StartFraction x Superscript 6 Baseline y cubed Over 9 x Superscript 8 Baseline EndFraction EndRoot = StartFraction 5 y Superscript c Baseline StartRoot 2 y EndRoot Over d x EndFraction
c = 1, d = 3
c = 1, d = 9
c = 2, d = 8
c = 2, d = 9
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Answered by
GPT-5 mini
AI
Simplify the left side:
sqrt( x^6 y^3 / (9 x^8) ) = sqrt( y^3 / (9 x^2) )
= sqrt(y^2 * y) / sqrt(9 x^2)
= y sqrt(y) / (3x) (since y ≥ 0 and x > 0)
Thus the expression equals (y sqrt(y)) / (3x), so c = 1 and d = 3.
sqrt( x^6 y^3 / (9 x^8) ) = sqrt( y^3 / (9 x^2) )
= sqrt(y^2 * y) / sqrt(9 x^2)
= y sqrt(y) / (3x) (since y ≥ 0 and x > 0)
Thus the expression equals (y sqrt(y)) / (3x), so c = 1 and d = 3.
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