Advertisements
Advertisements
рдкреНрд░рд╢реНрди
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
Advertisements
рдЙрддреНрддрд░
Let the two numbers be x and x - 4
Given that the difference of two numbers is 4.
By the given hypothesis, we have
`1/(x-4)-1/x=4/21`
`rArr(x-x+4)/(x(x-4))=4/21`
⇒ 84 = 4x(x – 4)
⇒ ЁЭСе2 - 4ЁЭСе - 21 = 0
⇒ ЁЭСе2 - 7ЁЭСе + 3ЁЭСе - 21 = 0
⇒ ЁЭСе(ЁЭСе - 7) + 3(ЁЭСе - 7) = 0
⇒ (ЁЭСе - 7)(ЁЭСе + 3) = 0
⇒ ЁЭСе = 7 ЁЭСЬЁЭСЯ ЁЭСе = -3 and
If x = -3, x – 4 = -3 - 4 = -7
Hence, required numbers are 3, 7 and -3, -7
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНтАНрди
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
Two squares have sides x cm and (x + 4) cm. The sum of this areas is 656 cm2. Find the sides of the squares.
The time taken by a person to cover 150 km was 2.5 hrs more than the time taken in the return journey. If he returned at a speed of 10 km/hr more than the speed of going, what was the speed per hour in each direction?
A girls is twice as old as her sister. Four years hence, the product of their ages (in years) will be 160. Find their present ages.
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Find the tow consecutive positive odd integer whose product s 483.
Solve the following quadratic equation by factorisation.
x2 + x – 20 = 0
Solve the following equation: 4x2 + 16x = 0
Solve the following equation: 4x2 - 13x - 12 = 0
Solve the following equation : x2 + 2ab = (2a + b)x
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
The area of right-angled triangle is 600cm2. If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.
Solve the following equation by factorization
x (2x + 1) = 6
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
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?
Solve the quadratic equation: x2 – 2ax + (a2 – b2) = 0 for x.
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
