Question
If (5x - 2y) = 170 and 4x:3y = 32:9, then find the
value of (3x² + y²).Solution
Given, 4x:3y = 32:9 Or, 4x × 9 = 3y × 32 Or, 36x = 96y So, x:y = 96:36 = 8:3 So, let the values of 'x' and 'y' be '8k' and '3k', respectively. ATQ, (5x - 2y) = 170 Or, 5 × 8k - 2 × 3k = 170 Or, 40k - 6k = 170 Or, 34k = 170 So, 'k' = 5 Therefore, values of 'x' and 'y' are 40 and 15, respectively. So, (3x² + y²) = (3 × 40² + 15²) = (3 × 1600 + 225) = (4800 + 225) = 5,025 Hence, option c.
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