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If y (3x - y) : x (4x + y) = 5 : 12, find (x2 + y2) : (x + y)2. Answer in proper explanation and i will mark you as the brainiest..... |
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Answer» Answer: 25/49 Step-by-step explanation: Given If y(3x-y):x(4x+y)= 5:12, then find the RATIO (x^2+y^2):(x+y)^2 So we need to find the ratio. So product of means is equal to product of extremes. So 12 y(3 x – y) = 5 x(4 x + y) 36xy – 12y^2 = 20x^2 + 5xy 36xy – 5xy = 20x^2 + 12 y^2 31xy = 20x^2 + 12y^2 20x^2 – 31xy + 12 y^2 = 0 20x^2 – 16 XY – 15 xy + 12y^2 = 0 4x(5x – 4y) – 3y(5x – 4y) = 0 5x – 4y = 0 4x – 3y = 0 5x = 4y 4x = 3y x = 4y / 5 x = 3y / 4 Now we need to find x ^2 + y^2 / (x + y)^2 Substituting for x we get x = 4 y/5 16 y^2 / 25 + y^2 / (9 y / 5)^2 41 y^2 / 25 / 81 y^2 / 25 = 41 / 81 When x =3 y/4 we get 9 y^2 / 16 + y^2 / (7y / 4)^2 = 25 y^2 / 16 / 49 y^2 / 16 = 25 / 49 |
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