Divide 11 into two parts such that the parts differ by 5/24.
What are the parts?
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(i) Let one part be x.
And the other part = x2
Therefore, according to equation
x2 + x = 42
⇒ x2 + x – 42 = 0
(ii) Let the positive odd number be x + 1
The other consecutive positive odd number = (x + 1) + 2 = x + 3
According to question,
(x + 1)(x + 3) = 143
⇒ x2 + 3x + x + 3 = 143
⇒ x2 + 4x + 3-143 = 0
⇒ x2 + 4x -140 = 0
(iii) Let the first number be x.
And the other consecutive number = x + 1
According to question,
x2 + (x + 1)2 = 313
⇒ x2 + x2 + 1 + 2x = 313
⇒ 2x2 + 2x + 1 – 313 = 0
⇒ 2x2 + 2x - 312 = 0
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