Math, asked by lochanalochana, 2 months ago

41 Rohan's mother is 26 years older than him. The product of their ages after 3 years
will be 360 years. Represented the above situation in the form of quadratic equation

Answers

Answered by BrainlyShadow01
33

To Find:-

  • Find the value of x.

Given:-

  • Rohan's mother is 26 years older than him. The product of their ages after 3 years will be 360 years.

Solution:-

\tt \: Rohan's \: \: mother \: \: is \: \: 26 \: \: years \: \: older \: \: than \: \: him \: .

\tt \: Let \: \: Rohan's \: \: age \: \: be \: \: " x "

\tt \: Rohan's \: \: mother \: \: age \: \: is " x + 26 "

\tt \: After \: \: 3 \: \: years \: \: their \: \: she \: \: will \: \: be

\tt \: Rohan's \: \: age = ( x + 3 )

\tt \: Rohan's \: \: mother \: \: age = ( x + 26 + 3 ) = ( x + 29 )

\tt \: The \: \: product \: \: of \: \: their \: \: ages \: \: after \: \: 3 \: \: years \: \: is \: \: 360 \: years.

\tt\implies \: ( x + 3 ) ( x + 29 ) = 360

\tt\implies \: { x }^{ 2 } + 29x + 3x + 87 = 360

\tt\implies \: { x }^{ 2 } + 32x - 273 = 0

\tt\implies \: { x }^{ 2 } + 39x - 7x - 273 = 0

\tt\implies \: x ( x + 39 ) - 7( x + 39 ) = 0

\tt\implies \: ( x + 39 ) ( x - 7 ) = 0

\tt\implies \: x = - 39 \: ; \: 7

\tt\implies \: x = 7

\tt \: Hence \: ,

  • \tt \: Rohan's \: \: age  = 7 \: years

  • \tt \: Mother's \: \: age = x + 26 = 33 \: years
Answered by mathdude500
3

\large\underline\purple{\bold{Solution :-  }}

Let Rohan's present age be 'x' years.

So, mother present age be 'x + 26' years.

After 3 years,

  • Rohan age be 'x + 3' years

  • Mother age be 'x + 29' years.

 \bigstar \:  \:  \red{ \rm \: According \:  to \:  statement }

  • The product of their ages after 3 years will be 360 years.

 \rm :  \implies \:(x + 3)(x + 29) = 360

 \rm :  \implies \: {x}^{2}  + 29x + 3x + 87 = 360

 \boxed{ \purple{ \rm :  \implies \: {x}^{2}  + 32x - 273 = 0}}

is the required expression.

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