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harkovskaia [24]
2 years ago
9

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

Mathematics
1 answer:
worty [1.4K]2 years ago
4 0

Answer:

(a)\ y = 4\ or\ y = -\frac{1}{2}

(b)\ x = 2 \ or\ x = -\frac{1}{4}

Step-by-step explanation:

Solving (a)

2y^2 - 7y  - 4 = 0

Expand

2y^2  +y - 8y  - 4 = 0

Expand

y(2y + 1)  -4(2y + 1) = 0

Factor out 2y + 1

(y -4)(2y + 1) = 0

Split

y - 4 =0\ or\ 2y + 1 = 0

Solve:

y = 4\ or\ y = -\frac{1}{2}

Solving (b):

2(2x)^2 - 7(2x) - 4 = 0

Compare the above with the equation in (a)

2y^2 - 7y  - 4 = 0

We have:

2x = y

So:

2x = 4 \ or\  2x = -\frac{1}{2}

Solve for x in both cases

x = 2 \ or\ x = -\frac{1}{4}

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