Question

the sum of two natural numbers is 8 and the sum of their reciprocals is 8/15.find the number.

Answer 1

Dear student,
$$\begin{gathered} lettheno.bexandy \\ thenx+y=8--\left(1\right) \\ \frac{1}{x}+\frac{1}{y}=\frac{8}{15}--\left(2\right) \\ \Rightarrow \frac{x+y}{xy}=\frac{8}{15} \\ \Rightarrow xy=15(putx+y=8from(1) \\ i.ey=\frac{15}{x}--(3) \\ put(3)in(1)toget \\ x+\frac{15}{x}=8 \\ \Rightarrow x^2+15=8x \\ \Rightarrow x^2-8x+15=0 \\ \Rightarrow x^2-5x-3x+15=0 \\ \Rightarrow x\left(x-5\right)-3\left(x-5\right)=0 \\ \Rightarrow \left(x-5\right)\left(x-3\right)=0 \\ \Rightarrow x=5\&y=3 \\ sotheno.are3\&5 \end{gathered}$$
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