Advertisements
Advertisements
Question
Divide 57 into two parts whose product is 680.
Advertisements
Solution
Let the two parts be x and (57-x)
According to the given condition,
`x(57-x)=680`
⇒`57x-x^2=680`
⇒`x^2-57x+680=0`
⇒`x^2-40x-17x+680=0`
⇒`x(x-40)-17(x-40)=0`
⇒`(x-40) (x-17)=0`
⇒`x-40=0 or x-17=0`
⇒`x=40 or x=17`
When `x=40`
`57-x=57-40=17`
When` x=17`
`57-x=57-17=40`
Hence, the required parts are 17 and 40.
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
`2x^2 – x + 1/8 = 0`
Solve the following quadratic equations by factorization:
4x2 + 5x = 0
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
(m – 3)x2 – 4x + 1 = 0
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
Solve the following quadratic equation by factorisation.
\[6x - \frac{2}{x} = 1\]
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
Solve the following equation: 25x (x + 1) = -4
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
Two pipes running together can 1 fill a cistern in 11 1/9 minutes. If one pipe takes 5 minutes more than the other to fill the cistern find the time when each pipe would fill the cistern.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
The product of two successive integral multiples of 5 is 300. Then the numbers are:
