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Tuition > Learn Tuition > If a + b : ab = 2 : 1, then find a :...
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If a + b : ab = 2 : 1, then find a : b.

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the equation can be simplified as follows:- (1/a)+(1/b)=2. so 1/b= 2- (1/a), simplifying by taking LCM 1/b=(2a-1)/a. thus, flipping over the numerator and denominator on both sides we get b= a/(2a-1) This shows that by putting the value of b, the ratio a:b= a/ which is equal...
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the equation can be simplified as follows:- (1/a)+(1/b)=2. so 1/b= 2- (1/a), simplifying by taking LCM 1/b=(2a-1)/a. thus, flipping over the numerator and denominator on both sides [formally called as invertendo] we get b= a/(2a-1) This shows that by putting the value of b, the ratio a:b= a/[a/(2a-1)] which is equal to (2a-1):1. therefore for every value you choose for 'a' the ratio a:b= (2a-1):1 read less
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The ratio a:b is not a constant . It depends on the variables.
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a + b = 2 a * b = 1 a = 1 b = 1 a : b = 1 : 1
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a + b = 2 ...........I a * b = 1 ...........II From equation II, we get a = 1/b .............III put this value in equation I ie. 1/b + b = 2 (1 + b*b) / b = 2 1 + b*b = 2b b*b - 2*b + 1 = 0 (b - 1)(b - 1) = 0 b - 1 = 0 b = 1 Put this...
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a + b = 2 ...........I a * b = 1 ...........II From equation II, we get a = 1/b .............III put this value in equation I ie. 1/b + b = 2 (1 + b*b) / b = 2 1 + b*b = 2b b*b - 2*b + 1 = 0 (b - 1)(b - 1) = 0 b - 1 = 0 b = 1 Put this value in equation III a = 1/1 a = 1 So, a : b = 1 : 1 read less
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