Advertisements
Advertisements
рдкреНрд░рд╢реНрди
The sum of a number and its reciprocal is 17/4. Find the number.
Advertisements
рдЙрддреНрддрд░
Let the number be ‘x’
According to the given hypothesis
`x+1/x=17/4`
`rArr(x^2+1)/x=17/4`
⇒ 4(ЁЭСе2 + 1) = 17ЁЭСе
⇒ 4ЁЭСе2 - 17ЁЭСе + 4 = 0
⇒ 4ЁЭСе2 - 16ЁЭСе - ЁЭСе + 4 = 0
⇒ 4ЁЭСе(ЁЭСе - 4) - 1(ЁЭСе - 4) = 0
⇒ ЁЭСе =1/4 ЁЭСЬЁЭСЯ ЁЭСе = 4
∴ The value of ЁЭСе = 4
APPEARS IN
рд╕рдВрдмрдВрдзрд┐рдд рдкреНрд░рд╢реНрди
Solve the following quadratic equation by factorization method : `x^2-5x+6=0`
The product of two successive integral multiples of 5 is 300. Determine the multiples.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 - 2\left( k + 1 \right)x + k^2 = 0\]
If the equation 9x2 + 6kx + 4 = 0 has equal roots, then the roots are both equal to
The value of c for which the equation ax2 + 2bx + c = 0 has equal roots is
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
Solve the following quadratic equation using formula method only
x2 - 6x + 4 = 0
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
Solve the equation 2x `-(1)/x` = 7. Write your answer correct to two decimal places.
Solve the following equation by factorization
x2 – 3x – 10 = 0
If x = p is a solution of the equation x(2x + 5) = 3, then find the value of p.
If the product of two positive consecutive even integers is 288, find the integers.
Solve the following equation by factorisation :
x2 + 6x – 16 = 0
Solve the following equation by factorisation :
2x2 + ax – a2= 0
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
