Question

plzzz ans....Quadratic equation....thnk u

Answer 1

2x articles cost = rs ( 5x + 54 )

then , cost of 1 article would be = rs ( 5x + 54 ) / 2x

x+2 articles cost = rs ( 10x - 4 )

then, cost of 1 article = rs ( 10x - 4 ) / x+2

since , both are same articles . Hence , we can equate the above equations

=> (5x+54) / 2x = (10x-4) / (x+2)

=> (5x+54)(x+2) = (10x-4)(2x)

=> 5x² + 10x + 54x + 108 = 20x² - 8x

=> 20x² - 5x² - 8x - 64x - 108 = 0

=> 15x² - 72x - 108 = 0

=> 3 ( 5x² - 24x - 36 ) = 0

=> 5x² - 24x - 36 = 0/3 = 0

=> 5x² - 30x + 6x - 36 = 0

=> 5x ( x - 6 ) + 6 ( x - 6 ) = 0

=> ( x - 6 ) ( 5x + 6 ) = 0

( x - 6 ) = 0 => x = 6

( 5x + 6 ) = 0 => x = -6/5

since , x cannot be in negative
therefore , x = 6

hope this helps

Answer 2

Hello Radhika

Your answer is.....

2x Costs ₹ ( 5x + 54 )

So 1 article costs
$\frac{(5x + 54)}{2x}$

Let this be equation (1)

Now,

( x + 2 ) articles costs ₹ ( 10x - 4 )

Then 1 article costs
$\frac{(10x - 4)}{x + 2}$

Let this be equation (2)

In question, it is given that both are costs same ,

so, Equation (1) = Equation (2)

$\frac{5x + 54}{2x} = \frac{10x - 4}{x + 2} \\ \\ (5x + 54) \times (x + 2) = (10x - 4) \times (2x) \\ \\ 5 {x}^{2} + 54x + 10x + 108 = 20 {x}^{2} - 8x \\ \\ 15 {x}^{2} - 72x - 108 = 0 \\ \\ 5 {x}^{2} - 24x - 36 = 0 \\ \\ 5 {x}^{2} - 30x + 6x - 36 = 0 \\ \\ 5x \times (x - 6) + 6 \times (x - 6) = 0 \\ \\ (5x + 6) \times (x - 6) = 0 \\ \\ x = 6 \: or \: \frac{ - 6}{5}$

x cannot be in negative forms

therefore ,
x = 6

Hope it helps