Advertisements
Advertisements
Question
The sum of a numbers and its positive square root is 6/25. Find the numbers.
Advertisements
Solution
Let the number be x
By the hypothesis, we have
`rArrx+sqrtx=6/25`
⇒ let us assume that x = y2, we get
`rArry^2+y=6/25`
⇒ 25𝑦2 + 25𝑦 − 6 = 0
The value of ‘y’ can be obtained by
`y=(-b+-sqrt(b^2-4ac))/(2a)`
Where a = 25, b = 25, c = −6
`rArry=(-25+-sqrt(625-600))/50`
`rArry=(-25+-35)/50`
`rArry=1/5` or `-11/10`
`x=y^2=(1/5)^2=1/25`
∴ The number x = `1/25`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Find two numbers whose sum is 27 and product is 182.
Solve the following quadratic equations by factorization:
`1/(x+4)-1/(x-7)=11/30` , x ≠ 4, 7
A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Solve:
x(x + 1) + (x + 2)(x + 3) = 42
Find the tow consecutive positive odd integer whose product s 483.
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 - 2\left( k + 1 \right)x + \left( k + 1 \right) = 0\]
Write the condition to be satisfied for which equations ax2 + 2bx + c = 0 and \[b x^2 - 2\sqrt{ac}x + b = 0\] have equal roots.
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
Solve the following equation:
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 5/2 , x ≠-1/2`
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solve equation using factorisation method:
(x + 1)(2x + 8) = (x + 7)(x + 3)
Find the values of x if p + 7 = 0, q – 12 = 0 and x2 + px + q = 0,
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Find the roots of the following quadratic equation by the factorisation method:
`2/5x^2 - x - 3/5 = 0`
Find the roots of the following quadratic equation by the factorisation method:
`3x^2 + 5sqrt(5)x - 10 = 0`
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
