Find the positive integral value of x if the fourth proportional of x, x + 1, 2x + 3 is y and y = 3x + 3.
3
Fourth proportional of x, (x+1), (2x+3) is y: \(x:(x+1) = (2x+3):y \Rightarrow y = \dfrac{(x+1)(2x+3)}{x}\).
Given \(y = 3x+3 = 3(x+1)\), so \(\dfrac{(x+1)(2x+3)}{x} = 3(x+1)\).
Dividing both sides by (x+1): \(\dfrac{2x+3}{x} = 3 \Rightarrow 2x+3 = 3x \Rightarrow x = 3\).
Hence, the positive integral value of x is 3.
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Important Questions from Fourth Proportional
The fourth proportional to the numbers 5, 6 and 8 is:
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If 162 ∶ x ∶∶ x ∶ 338, find the positive value of x.
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