Advertisements
Advertisements
рдкреНрд░рд╢реНрди
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
Advertisements
рдЙрддреНрддрд░
Let the numbers be x and x - 3
By the given hypothesis,
ЁЭСе2 + (ЁЭСе - 3)2 = 117
⇒ ЁЭСе2 + ЁЭСе2 + 9 - 6ЁЭСе - 117 = 0
⇒ 2ЁЭСе2 - 6ЁЭСе - 108 = 0
⇒ ЁЭСе2 - 3ЁЭСе - 54 = 0
⇒ ЁЭСе(ЁЭСе - 9) + 6(ЁЭСе - 9) = 0
⇒ (x - 9) (x + 6) = 0
⇒ x = 9 or x = -6
Considering positive value of x
x = 9, x - 3 = 9 - 3 = 6
∴ The two numbers be 9 and 6.
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers.
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.
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Find two consecutive multiples of 3 whose product is 648.
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 0
Solve the following quadratic equation by factorisation.
25m2 = 9
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
Solve the following quadratic equations by factorization:
\[9 x^2 - 6 b^2 x - \left( a^4 - b^4 \right) = 0\]
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}, x \neq - 1, \frac{1}{3}\]
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Solve the following equation by factorization
3(y2 – 6) = y(y + 7) – 3
Find two consecutive even natural numbers such that the sum of their squares is 340.
Rs. 7500 is divided equally among a certain number of children. Had there been 20 less children, each would have receive Rs 100 more. Find the original number of children.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:
