Advertisements
Advertisements
प्रश्न
Two natural number differ by 3 and their product is 504. Find the numbers.
Advertisements
उत्तर
Let the required numbers be x and (x+3) According to the question:
`x(x+3)=504`
⇒`x^2+3x=504`
⇒`x^2+3x-504=0`
⇒`x^2+(24-24)x-504=0`
⇒`x^2+24x-24x-504=0`
⇒`x(x-24)-21(x+24)=0`
⇒`(x+24)(x-21)=0`
⇒`x+24=0 or x-21=0`
`⇒x=-24 or x=21`
If x = -24, the numbers are `-24 and{(-24+3)=-21}`
If x =21, the numbers are `21 and {(21+3)=24}`
Hence, the numbers are `(-24,-21) and (21,24)`
APPEARS IN
संबंधित प्रश्न
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Determine whether the values given against the quadratic equation are the roots of the equation.
2m2 – 5m = 0, m = 2, `5/2`
Find the value of k for which the following equations have real and equal roots:
\[\left( k + 1 \right) x^2 - 2\left( k - 1 \right)x + 1 = 0\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
If p and q are the roots of the equation x2 – px + q = 0, then ______.
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
Solve the Following Equation : x2- x - a (a + 1) = o
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Three years ago, a man was 5 times the age of his son. Four years hence, he will be thrice his son's age. Find the present ages of the man and his son.
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
Divide 29 into two parts so that the sum of the square of the parts is 425.
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and Solve it to find the original cost of the books.
Solve the following equation by factorization
x2 – (p + q)x + pq = 0
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
