Advertisements
Advertisements
Question
The sum of a number and its square is 63/4. Find the numbers.
Solution
Let the number be x.
Given that the sum of x and its square = 63/4
⇒ x + ЁЭСе2 = 63/4
⇒ 4x + 4x2 - 63 = 0
⇒ 4x2 + 4x - 63 = 0
⇒ 4x2 + 4x - 63 = 0 ....................(i)
The value of x can be found by the formula
`x=(-b+-sqrt(b^2-4ac))/(2a)`
⇒ here a = 4, b = 4 and c = -63 from (i)
`x=(-4+-sqrt(16-4xx4xx-63))/(2xx4)`
`=(-4+-sqrt(16+16xx63))/(2xx4)`
`x=(-4+-sqrt(16+1008))/8`
Therefore,
`x=(-4+sqrt(16+1008))/8=7/2`
Or
`x=(-4-sqrt(16+1008))/8=-9/2`
∴ The values of x i. e. , the numbers is 7/2 , -9/2.
.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
5x2 - 3x - 2 = 0
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation : `"x"^2 - 4 sqrt 2 "x" + 6 = 0 `
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve the equation 3x² – x – 7 = 0 and give your answer correct to two decimal places.
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
