Advertisements
Advertisements
प्रश्न
The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.
Advertisements
उत्तर
Sum of two numbers = 9
Let first number = x
then second number = 9 – x
Now according to the condition,
(x)2 + (9 - x)2 = 41
⇒ x2 + 81 - 18x + x2 - 41 = 0
⇒ 2x2 - 18x + 40 = 0
⇒ x2 - 9x + 20 = 0 ...(Dividing by 2)
⇒ x2 - 4x - 5x + 20 = 0
⇒ (x - 4) -5(x - 4) = 0
⇒ (x - 4) (x - 5) = 0
Either x - 4 = 0,
then x = 4
or
x - 5 = 0,
then x = 5
(i) If x = 4, then first number = 4
and second number = 9 - 4 = 5
(ii) If x = 5, then first number = 5
ans second number = 9 - 5 = 4
Hence numbers are 4 and 5.
APPEARS IN
संबंधित प्रश्न
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
Solve for x :
`3/(x+1)+4/(x-1)=29/(4x-1);x!=1,-1,1/4`
Solve the following quadratic equations by factorization:
`(x - 5)(x - 6) = 25/(24)^2`
Solve the following quadratic equations by factorization:
`x^2 + (a + 1/a)x + 1 = 0`
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
