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Question

a) A positive number is divided into two parts, such that the sum of the squares of the two parts is 208. The square of the larger part is 8 times the smaller part. Taking x as the smaller part of the two parts, find the number.

b) Solve the following quadratic equation and give the answer correct to two significant figures:
4x27x+2=0
[6 MARKS]

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Solution

Each subpart: 3 Marks

a) Let smaller part be x.
Then, (larger part)2=8x
According to the question,
8x+x2=208x2+8x208=0
Now, x=8±824×1×(208)2×1=8±64+8322=8±29.932Either x=8+29.932 or x=829.932x=21.932=10.97 or x=37.932=18.97
Here, if the smaller part is 10.97, the larger part = 9.36, which is not possible. If smaller part is -18.97, the larger part = 151.76 which is not possible.
So, such numbers do not exist.

b)
We have, 4x27x+2=0
Using the quadratic formula
we get: x = b±b24ac2a
Now, x=7±494×4×22×4=7±49328=7±178=7±4.1238Either x=7+4.1238 or x=74.1238x=11.1238 or x=2.8778x=1.390 or x=0.359=0.36
Hence, x = 1.4 or 0.36 (upto two significance figures).

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