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A Solve the equation 2y2 – 7y – 4 = 0 . b Use your answer to part a to solve the equation 2(2x)2 _ 7(2x) _ 4 = 0. [5] 9

Sagot :

MrRoyal

Answer:

[tex](a)\ y = 4\ or\ y = -\frac{1}{2}[/tex]

[tex](b)\ x = 2 \ or\ x = -\frac{1}{4}[/tex]

Step-by-step explanation:

Solving (a)

[tex]2y^2 - 7y - 4 = 0[/tex]

Expand

[tex]2y^2 +y - 8y - 4 = 0[/tex]

Expand

[tex]y(2y + 1) -4(2y + 1) = 0[/tex]

Factor out 2y + 1

[tex](y -4)(2y + 1) = 0[/tex]

Split

[tex]y - 4 =0\ or\ 2y + 1 = 0[/tex]

Solve:

[tex]y = 4\ or\ y = -\frac{1}{2}[/tex]

Solving (b):

[tex]2(2x)^2 - 7(2x) - 4 = 0[/tex]

Compare the above with the equation in (a)

[tex]2y^2 - 7y - 4 = 0[/tex]

We have:

[tex]2x = y[/tex]

So:

[tex]2x = 4 \ or\ 2x = -\frac{1}{2}[/tex]

Solve for x in both cases

[tex]x = 2 \ or\ x = -\frac{1}{4}[/tex]

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