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Question

Solve 16y2 - 20y + 98y2 + 12y + 21 = 4y - 52y + 3

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Solution

Let:16y2-20y+98y2+12y+21=4y-52y+3=k (x0)If we multiply both the terms of the second ratio by 4y, we would obtain the first two terms in each of the antecedents and consequents of the first ratio.

Now, on multiplying both the terms of the second ratio by 4y, we get:16y2-20y+98y2+12y+21=4y4y-54y2y+3=kBy the theorem on equal ratios, we get: 16y2-20y+9-4y4y-58y2+12y+21-4y2y+3=k16y2-20y+9-16y2+20y8y2+12y+21-8y2-12y=k921=kNow,4y-52y+3=92184y-105=18y+2766y=132y=2

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