Question
If (7x + 5y) = 206 and 3x:2y = 27:16, then find the
value of (x² + 2y²).Solution
Given, 3x:2y = 27:16 Or, 3x × 16 = 2y × 27 Or, 48x = 54y So, x:y = 9:8 So, let the values of 'x' and 'y' be '9k' and '8k', respectively. ATQ, (7x + 5y) = 206 Or, 7 × 9k + 5 × 8k = 206 Or, 63k + 40k = 206 Or, 103k = 206 So, 'k' = 2 Therefore, values of 'x' and 'y' are 18 and 16, respectively. So, (x² + 2y²) = (18² + 2 × 16²) = (324 + 2 × 256) = (324 + 512) = 836 Hence, option a.
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