Math, asked by Braɪnlyємρєяσя, 5 months ago

\huge \fbox \red{❥ Question}


The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

Answers

Answered by rapunzel4056
8

Answer:

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Let the present age of Rehman = x

∴ 3 years ago Rehman’s age = (x – 3) years

∴5 years later Rehman’s age = (x + 5) years

Now, according to the condition,

1/(x – 3 ) + 1/(x + 5) = 1/3

→(x + 5 + x – 3)/(x – 3)(x + 5) = 1/3

→(2x + 2)/(x2 – 3x +5x – 15) = 1/3

→x2 + 2x – 15 = 6x + 6

→x2 – 4x – 21 = 0

→(x + 3)(x – 7) = 0

Either, x + 3 = 0 Or, x – 7 = 0

Thus, x = 7 or – 3; but age cannot be negative. Hence the present age of Rehman is 7 years.

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Anonymous: thanks ☺️
MartialMonk: great answer....keep it up✌✌
rapunzel4056: Welcome
rapunzel4056: Thanks!!
Answered by Anonymous
35

Question

The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.

solution

Let Rehman's present age be X years.

Rehamna's age 3 years ago =( x-3) years

Rehman's age after 5 years= ( x+5) years

According to the question

   \sf{\to\frac{1}{(x - 3)}  +  \frac{1}{( x + 5)}  =  \frac{1}{3} } \\  \\  \sf{ \to \:  \frac{x + 5 + x - 3}{(x - 3)(x + 5)} } =  \frac{1}{3}  \\  \\  \sf{ \to \frac{2x + 2}{ {x}^{2}  + 2x - 15}  =  \frac{1}{3} } \\  \\  \sf{ \to \:  {x}^{2}  + 2x - 15 = 6x + 6} \\  \\  \sf { \to \: {x}^{2}  - 4x - 21 = 0 } \\  \\ \sf{ \underline{ D =  {b}^{2}  - 4ac}} \\  \\ \sf{ \to \: D =  }100 \\  \\  \sf{   : \implies \: x =  \frac{ - b +  \sqrt{D} }{2a} \: or  \:  \frac{ - b -  \sqrt{D} }{2a} } \\  \\  \sf \to \: x =  \frac{4 + \sqrt{100} }{2}   \: or \: \:   \frac{4 -  \sqrt{100} }{2}  \\  \\  \sf{ \to \: x = 7 \: or \:  - 3}

therefore the present age of Rehman is 7 years ..

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Anonymous: umm...I'm commenting under my answer to just check if comments are still visible or not...
rapunzel4056: Oh...yeah
Anonymous: omg ...cant believe my eyes ...that we can again comment under the answer
Anonymous: I'm surprised
Anonymous: ohh! that's amazing ☺️
Anonymous: Hehe
MartialMonk: great and nice answer!!!
rapunzel4056: Yeah
Anonymous: thanks :)
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