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Posted by Naresh Krish 6 years, 5 months ago
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Sia ? 6 years, 5 months ago
Let the numbers be x and 15 - x.
According to question,
{tex}\frac { 1 } { x } + \frac { 1 } { 15 - x } = \frac { 3 } { 10 }{/tex}
{tex}\Rightarrow \quad \frac { 15 - x + x } { x ( 15 - x ) } = \frac { 3 } { 10 }{/tex}
{tex}\Rightarrow \quad \frac { 15 } { x ( 15 - x ) } = \frac { 3 } { 10 }{/tex}
Cross multiply,
{tex}\Rightarrow{/tex}{tex}150=3x(15-x){/tex}
{tex}\Rightarrow{/tex} {tex}150=45x-3x^2{/tex}
{tex}\Rightarrow 150=3(15x-x^2){/tex}
{tex}\Rightarrow{/tex} x2 - 15x + 50 = 0
{tex}\Rightarrow{/tex} x2 - 10x - 5x + 50 = 0
{tex}\Rightarrow{/tex} x(x - 10) - 5(x -10) = 0
{tex}\Rightarrow{/tex} (x - 10)(x - 5) = 0
{tex}\Rightarrow{/tex} x - 10 = 0 or, x - 5 = 0 {tex}\Rightarrow{/tex} x = 10 or, x = 5
Therefore, numbers are 10 and 5
Posted by Ayush Manav 7 years, 9 months ago
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Sia ? 6 years, 5 months ago
Let the origin be O and the coordinates of the origin are (0,0)
We can find the distance of P from the origin by using the distance formula, i.e.
OP = {tex}\sqrt{x^2 + y^2}{/tex}
Posted by Sakshi Chauhan 7 years, 9 months ago
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Aryan Nachiketh 7 years, 9 months ago
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Sia ? 6 years, 6 months ago
Assume denominator = x then, numerator = x - 1
{tex}\therefore{/tex} Fraction = {tex}\frac{x - 1}{x}{/tex}
According to given situation, we have
{tex}\frac{x - 1 + 3}{x + 3}{/tex} = {tex}\frac{x - 1}{x}{/tex} + {tex}\frac{3}{28}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac{x + 2}{x + 3}{/tex} - {tex}\frac{x - 1}{x}{/tex} = {tex}\frac{3}{28}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac { ( x + 2 ) x - ( x - 1 ) ( x + 3 ) } { ( x + 3 ) x }{/tex} = {tex}\frac{3}{28}{/tex}
{tex}\Rightarrow{/tex}{tex}\frac { x ^ { 2 } + 2 x - \left( x ^ { 2 } + 2 x - 3 \right) } { x ^ { 2 } + 3 x }{/tex} = {tex}\frac{3}{28}{/tex}
{tex}\Rightarrow{/tex}3{tex}\times{/tex}28 = 3(x2 + 3x)
{tex}\Rightarrow{/tex}x2 + 3x - 28 = 0
Factorize the above quadratic equation, we get
{tex}\Rightarrow{/tex}(x + 7)(x - 4) = 0 {tex}\Rightarrow{/tex}x = -7 or x = 4
Rejecting x = -7 {tex}\therefore{/tex}x = 4
{tex}\therefore{/tex} Fraction is {tex}\frac{4 - 1}{4}{/tex} = {tex}\frac{3}{4}{/tex}
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Royal Sher Gill 7 years, 9 months ago
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Nyayir Riba 7 years, 9 months ago
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