The sum of two numbers is …
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Sia ? 6 years, 5 months ago
Let the two numbers are x and 8 - x.
According to question,
{tex}15\left( {\frac{1}{x} + \frac{1}{{8 - x}}} \right) = 8{/tex}
{tex} \Rightarrow 15\left( {\frac{{8 - x + x}}{{x(8 - x)}}} \right) = 8{/tex}
{tex} \Rightarrow {/tex} {tex}15 \times 8=8x(8-x){/tex}
{tex} \Rightarrow 15 = \frac{{8x}}{8}(8 - x){/tex}
{tex} \Rightarrow {/tex} 15 = x(8 - x)
{tex} \Rightarrow {/tex} 15 = 8x - x2
{tex} \Rightarrow {/tex} x2 - 8x + 15 = 0
Factorise the equation,
{tex} \Rightarrow {/tex} x2 - 5x - 3x + 15 = 0
{tex} \Rightarrow {/tex} x(x - 5) - 3(x - 5) = 0
{tex} \Rightarrow {/tex} (x - 5)(x - 3) = 0
{tex} \Rightarrow {/tex} x = 5 or x = 3
Hence, required numbers are 3 and 5.
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