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dmitriy555 [2]
3 years ago
12

What are the solutions of the equation 9x^4 – 2x^2 – 7 = 0? Use u substitution to solve.

Mathematics
1 answer:
Debora [2.8K]3 years ago
8 0
9x^4 - 2x^2 - 7 = 0 \\ \text{substitution: }  x^2=t, \ \ t\ \textgreater \ 0\\ 9t^2-2t-7\ \textgreater \ 0 \\ D=b^2-4ac=(-2)^2-4*9*(-7)=4+252 = 256 \\ t_{1,2}= \frac{-bб \sqrt{D} }{2a}= \frac{2б 16 }{18} \\ t_1=- \frac{14}{18} \ \ \ \ \O \\  \boxed{t_2=1} \\ \\x^2=1\\x=б \sqrt{1} \\ x=б1

Answer: x=-1, x=1
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The stone would take approximately 10.107 seconds to fall 500 meters.

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According to the statement of the problem, the following relationship of direct proportionality is built:

t \propto y^{1/2}

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t - Time spent by the stone, measured in seconds.

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First, the proportionality constant is determined by clearing the respective variable and replacing all known variables:

k = \frac{t}{y^{1/2}}

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