(a) Solve the equation 6-V3+2x-2x+3 forx. b) Solve the following equation in the

Question

(a) Solve the equation 6-V3+2x-2x+3 forx. b) Solve the following equation in the variable x by factoring 4x4 +15x2-4-0 c) (similar to problem #116) A large pond is stocked with fish. The fish population P() is modeled by the parabolic equation P(t) 212 -32t +258, where t is the number of days since the fish were first introduced into the pond. How many days will it take for the fish population to reach 162? Give reasoning for the two answers How many days will it take for the fish population to reach the minimum population? What is the minimum population? Show, also all the above answers by graphing the associated parabola modeling the fish population

Explanation / Answer

a) 6 - sqrt ( 3 + 2x ) = 2x + 3

subtracting 6 from both sides

- sqrt ( 3 + 2x ) = 2x - 3

squaring both sides

{- sqrt ( 3 + 2x )}^2 = { 2x - 3 }^2

3 + 2x = 4x^2 + 9 - 12x

4x^2 - 14x + 6 = 0

x = 1/2

b) 4x^4 + 15x^2 - 4 = 0

( 4x^2 - 1 ) ( x^2 + 4 ) = 0

4x^2 - 1 = 0

x^2 = + - 1/2

x^2 + 4 = 0

x^2 = - 4

x = +- 2i

solution are

x = +1/2 , -1/2 , + 2i , - 2i

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