Advertisements
Advertisements
Question
The sum of a number and its reciprocal is `2 9/40`. Find the number.
Advertisements
Solution
Let the number be A. Then as per the question,
`"A" + 1/ "A" = 2 9/40`
⇒ `"A"^2 + 1 - 89/40 "A" = 0`
⇒ 40 A2 + 40 - 89 A=0
⇒ 40A2 - 89A + 40 = 0
⇒ 40 A2 - 64A - 25A + 40 = 0
⇒ 8A (5A - 8) - 5 (5A-8) = 0
⇒ (8A - 5)(5A - 8) = 0
⇒ A = `5/8 , 8/5`
APPEARS IN
RELATED QUESTIONS
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
Divide 57 into two parts whose product is 680.
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}, x \neq - 1, \frac{1}{3}\]
If ax2 + bx + c = 0 has equal roots, then c =
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.
Solve the equation x4 + 2x3 - 13x2 + 2x + 1 = 0.
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
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
