Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
Advertisements
рдЙрддреНрддрд░
Let the whole number be x as it is decreased by 20
⇒ (x - 20) = 69. (1/2)
⇒ ЁЭСе. 20 = 69. (1/ЁЭСе)
⇒ ЁЭСе(ЁЭСе - 20) = 69
⇒ ЁЭСе2 - 20ЁЭСе - 69 = 0
⇒ ЁЭСе2 - 23 + 3ЁЭСе - 69 = 0
⇒ ЁЭСе(ЁЭСе - 23) + 3(ЁЭСе - 623) = 0
⇒ (x - 23) (x + 3) = 0
⇒ x = 23; x = -3
As the whole numbers are always positive, x = -3 is not considered.
∴ The whole number x = 23.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
Solve the following quadratic equations by factorization:
x2 + 2ab = (2a + b)x
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
`x^2-6x+3=0`
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Find the values of k for which the roots are real and equal in each of the following equation:
\[kx\left( x - 2\sqrt{5} \right) + 10 = 0\]
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
The area of the isosceles triangle is 60 cm2, and the length of each one of its equal side is 13cm. Find its base.
There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path.
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
Solve the following equation by factorization
3(x – 2)2 = 147
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
Solve the quadratic equation by factorisation method:
x2 – 15x + 54 = 0
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
