the different of two number is 4 if the difference of their reciprocal is 4/21,then find two numbers
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Heya !!!
Let two numbers be X and Y.
According to question,
Difference of two numbers =>4
X - Y = 4 --------(1)
Reciprocal of X is 1/X and Reciprocal of Y is 1/Y.
1/X - 1/Y = 4/21
Y - X / XY = 4/21
21(Y - X ) = 4XY
21Y - 21X = 4XY -------(2)
From equation (1) we get,
X - Y = 4
X = 4 + Y ------(3)
Putting the value of X in equation (2)
21Y - 21X = 4XY
21Y - 21 ( 4 + Y) = 4(4+Y) × Y
21Y - 84 - 21Y = (16 + 4Y)Y
-84 = 16Y + 4Y²
4Y² + 16Y + 84 = 0
4Y² + 28Y - 12Y + 84 = 0
4Y ( Y + 7 ) - 12 ( Y + 7) = 0
( Y + 7) ( 4Y - 12) = 0
(Y+7) = 0 OR (4Y-12) = 0
Y = -7 OR Y = 12/4 = 3
Putting Y = 3 in equation (3)
X = 4 +Y
X = 4+3 = 7
Hence,
Two numbers are 7 and 3.
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
Let two numbers be X and Y.
According to question,
Difference of two numbers =>4
X - Y = 4 --------(1)
Reciprocal of X is 1/X and Reciprocal of Y is 1/Y.
1/X - 1/Y = 4/21
Y - X / XY = 4/21
21(Y - X ) = 4XY
21Y - 21X = 4XY -------(2)
From equation (1) we get,
X - Y = 4
X = 4 + Y ------(3)
Putting the value of X in equation (2)
21Y - 21X = 4XY
21Y - 21 ( 4 + Y) = 4(4+Y) × Y
21Y - 84 - 21Y = (16 + 4Y)Y
-84 = 16Y + 4Y²
4Y² + 16Y + 84 = 0
4Y² + 28Y - 12Y + 84 = 0
4Y ( Y + 7 ) - 12 ( Y + 7) = 0
( Y + 7) ( 4Y - 12) = 0
(Y+7) = 0 OR (4Y-12) = 0
Y = -7 OR Y = 12/4 = 3
Putting Y = 3 in equation (3)
X = 4 +Y
X = 4+3 = 7
Hence,
Two numbers are 7 and 3.
★ ★ ★ HOPE IT WILL HELP YOU ★ ★ ★
ziya02:
tq
Answered by
5
let larger number be x and smaller be y then x-y=4and,1/x-1/y=4/21x-y/xy=4/214/xy=4/21xy= 21x+y = √[x-y]²+4xy = √4²+4×21 = √16+84 = √100 =10thus we have x-y=4 equation 1 x+y=10 equation 2on solving 1 and 2 we get x=7 and y=-3 or we can also take √100=-10then we have x-y = 4 and x+y = -10 on solving we get x = -3 and y = -7hence required numbers are 7 and 3 and -3 and -7
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