Advertisements
Advertisements
प्रश्न
Find three consecutive odd integers, the sum of whose squares is 83.
Advertisements
उत्तर
Let the three numbers be x, x + 2, x + 4
According to statements,
(x)2 + (x + 2)2 + (x + 4)2 = 83
⇒ x2 + x2 + 4x + 4 + x2 + 8x + 16 = 83
⇒ 3x2 + 12x + 20 = 83
⇒ 3x2 + 12x + 20 - 83 = 0
⇒ 3x2 + 12x - 63 = 0
⇒ x2 + 4x - 21 = 0
⇒ x2 + 7x - 3x - 21 = 0
⇒ x(x + 7) -3(x + 7) = 0
⇒ (x - 3)(x + 7) = 0
Either x - 3 = 0,
then x = 3
or
x + 7 = 0,
then x = -7
∴ Number will be 3, 3 + 2, 3 + 4 = 3, 5, 7
or
Numbers will be -7, -7 + 2, -7 + 4 = -7, -5. -3.
APPEARS IN
संबंधित प्रश्न
Find two consecutive positive integers, sum of whose squares is 365.
Solve the following quadratic equations by factorization:
6x2 - x - 2 = 0
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
A two digit number is four times the sum and 3 times the product of its digits, find the number.
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
Solve the following equation by factorization
6p2+ 11p – 10 = 0
Find two consecutive odd integers such that the sum of their squares is 394.
A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/h more. Find the original speed of the train.
