Question

⭐The sum of two numbers is 9 and the sum of their reciprocal is 1/2.Find the numbers.⭐

CLASS 10 CHAPTER :QUADRATIC EQUATIONS

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Answer 1

卄乇ㄚ 千尺丨乇几ⅅ

卄乇尺乇 丨丂 ㄚㄖ凵尺

卂几丂山乇尺

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⊙ Let the 1st number be x

⊙ Then the 2nd number is (9-x)

so, their reciprocal is :-

$\frac{1}{x} + \frac{1}{9 - x} = \frac{1}{2}$

⊙
$\frac{9 - x + x}{x(9 - x)} = \frac{1}{2}$

$\frac{9}{9x - x {}^{2} } = \frac{1}{2}$

$9x - x {}^{2} - 18 = 0$

$3x - {x}^{2} + 6x - 18 = 0$

splitting the equation.

$x(3 - x) + 6(x - 3) = 0 \\ \\ x(3 - x) - 6(3 - x) = 0$

$(3 - x)(x - 6)$

so, x = 3 & 6.

$<h1 > hope it helps$

$<marquee > prabhudutt$

Answer 2

Let the two numbers be x and y.

Then, According to the question,

x + y = 9. --> ( i )

1 / x + 1 / y = 1 / 2.

( x + y ) / xy = 1 / 2

2 x + 2y = x y ---> ( ii )

Solving ( i ) and ( ii ),

x = 9 - y. ---> ( a )

Putting value of x in equation ( ii ).,

2 ( 9 - y ) + 2 y = ( 9 - y ) y

18 - 2y + 2y = 9y - y ²

18 = 9 y - y ²

y² - 9y + 18 = 0.

y ² - 6y - 3 y + 18 = 0

y ( y - 6 ) - 3 ( y - 6 ) = 0

( y - 3 ) ( y - 6 ) = 0

y = 3, 6.

Since, x = 9 - y

x = 9 - 3 = 6.

Or

x = 9 - 6 = 3.

When y = 3, x = 6 and when y = 6, x = 3.