Advertisements
Advertisements
प्रश्न
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Advertisements
उत्तर
Let the two consecutive positive odd numbers be x and (x+2).
According to the given condition
`x^2+(x+2)^2=514`
⇒`x^2+x^2+4x+4=514`
⇒`2x^2+4x-510=0`
⇒`x^2+2x-255=0`
⇒`x^2+17x-15x-255=0`
⇒`x(x+17)-15(x+17)=0`
⇒`(x+17)(x-15)=0`
⇒`x+17=0` or `x-15=0`
⇒`x=-17 or x-15`
∴`x=15` (x is a positive odd number)
When `x=15`
`x+2=15+2=17`
Hence, the required positive integers are 15 and 17.
APPEARS IN
संबंधित प्रश्न
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
`(x+3)/(x+2)=(3x-7)/(2x-3)`
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Let us find two natural numbers which differ by 3 and whose squares have the sum 117.
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 +bx + 1 = 0 having real roots is
If the sum of the roots of the equation \[x^2 - \left( k + 6 \right)x + 2\left( 2k - 1 \right) = 0\] is equal to half of their product, then k =
Solve the following equation :
`("x" - 1)/("x" - 2) + ("x" - 3)/("x" - 4) = 3 1/3`
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3x + 2 = 0; x = 2, x = -1
If the product of two consecutive even integers is 224, find the integers.
The speed of a boat in still water is 11 km/ hr. It can go 12 km up-stream and return downstream to the original point in 2 hours 45 minutes. Find the speed of the stream
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
Which of the following is correct for the equation `1/(x - 3) - 1/(x + 5) = 1`?
