Advertisements
Advertisements
рдкреНрд░рд╢реНрди
The sum of two numbers is 48 and their product is 432. Find the numbers?
Advertisements
рдЙрддреНрддрд░
Given the sum of two numbers is 48
Let the two numbers be x and 48 – x also given their product is 432.
Hence x(48 - x) = 432
⇒ 48x - x2 = 432
⇒ 48x - x2 - 432 = 0
⇒ ЁЭСе2 - 48ЁЭСе + 432 = 0
⇒ ЁЭСе2 - 36ЁЭСе - 12ЁЭСе + 432 = 0 [By method of factorisation]
⇒ ЁЭСе(ЁЭСе - 36) - 12(ЁЭСе - 36) = 0
⇒ (ЁЭСе - 36)(ЁЭСе - 12) = 0
⇒ x = 36 or x = 12
∴ The two numbers are 12, 36.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve the following quadratic equations by factorization:
25x(x + 1) = -4
Solve the following quadratic equations by factorization:
3x2 − 14x − 5 = 0
The sum of a numbers and its positive square root is 6/25. Find the numbers.
Two numbers differ by 3 and their product is 504. Find the number
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
Find the tow consecutive positive odd integer whose product s 483.
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
Solve the following quadratic equation using formula method only
6x2 + 7x - 10 = 0
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solve the following equation by factorization
`(x + 2)/(x + 3) = (2x - 3)/(3x - 7)`
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
Find the roots of the quadratic equation x2 – x – 2 = 0.
