Question

the sum of natural number and it's resipocal is 50/7 , find the numbers​

Answer 1

GIVEN :–

• The sum of natural number and it's resipocal is 50/7.

TO FIND :–

• Number = ?

SOLUTION :–

• Let the number is 'x'.

$\\ \bf \implies x + \dfrac{1}{x} = \dfrac{50}{7}$

$\\ \bf \implies x + \dfrac{1}{x} = \dfrac{50}{7}$

$\\ \bf \implies \dfrac{ {x}^{2} + 1}{x} = \dfrac{50}{7}$

$\\ \bf \implies 7({x}^{2} + 1) = 50x$

$\\ \bf \implies 7{x}^{2} + 7 = 50x$

$\\ \bf \implies 7{x}^{2} - 50x +7 = 0$

$\\ \bf \implies 7{x}^{2} - 49x - x +7 = 0$

$\\ \bf \implies 7x(x - 7) - 1(x - 7)= 0$

$\\ \bf \implies (7x - 1)(x - 7)= 0$

$\\ \large \implies{ \boxed{ \bf x = 7, \dfrac{1}{7}}}$

• Hence , The numbers are 7 and 1/7.

Answer 2

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Given :- }}}$

$\textsf{ \to The sum of a natural number and its} \\\textsf{ reciprocal is 50/7.}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: To \ Find :- }}}$

$\textsf{ \to The two numbers.}$

$\Large\underline{\underline{\red{\sf \purple{\maltese}\:\: Answer :- }}}$

Let us take the first number be x , then the second number will be 1/x .

$\underline{\boldsymbol{\purple{ According\ to \ the \ Question :- }}}$

$\sf:\implies \pink{ x + \dfrac{1}{x}= \dfrac{50}{7}}\\\\\sf:\implies \dfrac{x^2 + 1}{x}=\dfrac{50}{7}\\\\\sf:\implies 7( x^2 + 1)= 50x \\\\\sf:\implies 7x^2 + 7 = 50x \\\\\sf:\implies 7x^2-50x +7=0 \\\\\sf:\implies 7x^2 -49x - x +7 = 0 \\\\\sf:\implies 7x( x -7)-1(x-7) = 0\\\\\sf:\implies (7x-1)(x-7) = 0\\\\\sf:\implies \pink{\boxed{\mathfrak{ x = 7 , \dfrac{1}{7}}}}$

$\underline\blue{\sf Hence \ the \ required \ answer \ is \textsf{\textbf{7 or }}\dfrac{\textsf{\textbf{1}}}{\textsf{\textbf{7}}}}$

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