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Sia ? 6 years, 6 months ago
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Yogita Ingle 7 years, 3 months ago
7265 × 7265 - 7265 × 265
= 7265(7265 - 265)
= 7265(7000)
= 50855000
Posted by Kuljeet Singh Solanki 7 years, 3 months ago
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Posted by Nurav Nurav 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
F(x)=x2-x-4
here a=1,b=-1,c=-4
Now {tex}\mathrm\alpha\;\mathrm{and}\;\mathrm\beta{/tex} are zeros of f(x)
Sum of zeroes = α + β {tex}=-\frac ba{/tex}=-{tex}\frac{-1}{1}{/tex}=1
Product of the zeroes = αβ = {tex}\frac ca{/tex}={tex}\frac{-4}{1}=-4{/tex}
{tex}\frac1{\mathrm\alpha}+\frac1{\mathrm\beta}-\mathrm{αβ}=\frac{\mathrm\alpha+\mathrm\beta-\mathrm\alpha^2\mathrm\beta^2}{\mathrm{αβ}}=\frac{1-(-4)^2}{-4}{/tex}
{tex}=\frac{1-16}{-4}=\frac{-15}{-4}=\frac{15}4{/tex}
Posted by Siddhant Chaudhry 7 years, 3 months ago
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Posted by Money Kanwar 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
Let numerator of fraction is x and denominator is y.
Let the fraction be {tex}\frac { x } { y }.{/tex}
Then, according to the given conditions, we have
If 1 is added to both numerator and denominator then fraction becomes {tex}\frac { 4 } { 5 }{/tex}.
{tex}\frac { x + 1 } { y + 1 } = \frac { 4 } { 5 } {/tex}
{tex}\Rightarrow{/tex} 5x +5 =4y + 4
{tex}\Rightarrow{/tex} 5x - 4y + 1=0 ...... (i)
If 5 is subtracted from both numerator and denominator, the fraction becomes {tex}\frac { 1 } {2}{/tex}.
{tex}\frac { x - 5 } { y - 5 } = \frac { 1 } { 2 }{/tex}
{tex}\Rightarrow{/tex} 2x - 10 = y - 5
{tex}\Rightarrow{/tex} 2x - y - 5=0 ........ (ii)
From (i) and (ii)
By using cross-multiplication, we have
{tex}\frac { x } { - 4 \times - 5 - ( - 1 ) \times 1 } = \frac { - y } { 5 \times - 5 - 2 \times 1 } = \frac { 1 } { 5 \times - 1 - 2 \times - 4 }{/tex}
{tex}\Rightarrow \quad \frac { x } { 20 + 1 } = \frac { y } { 25 + 2 } = \frac { 1 } { - 5 + 8 }{/tex}
{tex}\Rightarrow \quad \frac { x } { 21 } = \frac { y } { 27 } = \frac { 1 } { 3 } {/tex}
{tex}\Rightarrow x = \frac { 21 } { 3 } = 7 \text { and } y = \frac { 27 } { 3 } = 9{/tex}
Hence, the given fraction is 7/9.
Posted by Jayant Arora 6 years, 6 months ago
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Sia ? 6 years, 6 months ago
{tex}\frac{x}{2}{/tex} + y = 0.8
{tex}\Rightarrow{/tex} x + 2y = 1.6
{tex}\Rightarrow{/tex} x = 1.6 - 2y ...........(i)
and {tex}\frac{7}{x+\frac{y}{2}}=10{/tex}
{tex} \Rightarrow \frac{14}{2 x+y}{/tex} = 10
{tex}\Rightarrow{/tex} 20x + 10y = 14
{tex}\Rightarrow{/tex} 10x + 5y = 7 ..........(ii)
Put (i) in (ii), we get
10(1.6 - 2y) + 5y = 7
{tex}\Rightarrow{/tex} 16 - 20y + 5y = 7
{tex}\Rightarrow{/tex} -15y = -9
{tex}\Rightarrow{/tex} y = {tex}\frac{9}{15}{/tex} = 0.6
Put y = 0.6 in equation (i), we get
x = 1.6 - 2(0.6)
x = 0.4
Hence x = 0.4 and y = 0.6 is the solution of given system of equations.
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Posted by Ziya Ferzin 5 years, 8 months ago
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Sia ? 6 years, 6 months ago
We have, (3 × 5 × 7) + 7 = 105 + 7 = 112
Prime factors of 112 = 2 × 2 × 2 × 2 × 7 = 24 {tex} \times {/tex} 7
So, it is the product of prime factors 2 and 7, i.e. it has factors other than 1 and itself. Hence, it is a composite number.
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Shubham Prajapati 7 years, 3 months ago

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Divya Keshav 7 years, 2 months ago
0Thank You