please help me.............answer in detail
Answers
I myself am weak in maths and want third, fifth and second question.......
hey friend ,
here is ur answer
1) 3x ² + ( k- 3 )x + 9 = 0
3 ( 3) ² + ( k-3) 3 + 9 = 0 [ put x = 3 ]
3 x 9 + 3k - 9 + 9 = 0 [ multiply 3 by ( k-3 ) u get 3k - 9 ]
27 + 3k = 0 {as we know (-) x ( +) = ( - ) so [-9] and [+9] will be 0 }
3k = -27 [ get 27 to the place of 0 it will become -27 ]
k = - 27 / 3 [ divide 3 with -27]
k = -9
u can cross check the answer if there are any mistakes
2) There is a difference of one in consecutive positive integers
let 1 st integer = x
second be = (x + 1 )
give that sum of squares is 365
∴ ( 1st integer )² + ( 2nd integer )² = 365
∴ ( x )² + ( x + 1)² = 365
∴ x ² + x² + 1² + 2 × x + 1 = 365
∴ 2x² + 1 + 2x = 365
∴ 2x² + 2x + 1 - 365 = 0
∴ 2x² + 2x - 364 = 0
∴ 2 ( x² + x - 182 ) = 0
∴ x² + x - 182 = 0 / 2
∴ x² + x - 182 = 0
we factorize by splitting the middle term method
x² + 14x - 13x - 182 = 0
x( x+ 14 ) - 13 ( x+ 14 ) = 0
( x + 14 ) ( x - 13) = 0
x + 14 = 0 x - 13 = 0
x = - 14 x = 13
so the root of the give equation are x = -14 and x = 13
since we have to find positive integers we take x = 13
1st number = 13
2nd number = 1 + x
= 1 + 13
= 14
5) Let the speed of train be x km/ hr
NORMAL SPEED
Distance = 360 km
Speed = x km/hr
Speed = distance / time
∴ x = 360 / time
∴ time = 360 / x
Speed 5 km/ hr more
distance = 360 km
speed = ( x + 5 ) km /hr
time = ( 360 / x ) - 1
now ,
speed = distance / time
( x + 5) = 360 / ( 360 / x ) - 1
( x+ 5 ) ( 360 / x - 1) = 480 ..........( 1)
from (1)
( x+ 5) ( 360 / x-1 ) = 360
( x+ 5) ( 360 - x / x ) = 360
( x + 5 ) ( 360 - x ) = 360 x
x ( 360 - x ) + 5 ( 360 - x ) = 360 x
360 x - x² + 5 ( 360 ) - 5 x = 360 x
360 - x² + 1800 - 5 x = 360 x
360 x - x² + 1800 - 5x - 360x = 0
- x² - 5x - 360x + 360x + 1800x = 0
- x² - 5x + 1800 = 0
∴ 0 = x² + 5x - 1800
∴ x² + 5x - 1800 = 0
we factorize by splitting the middle term method
x² + 45x - 40x - 1800 = 0
x ( x+ 45 ) - 40 ( x + 45) = 0
( x + 45 ) ( x - 40 ) = 0
x + 45 = 0 x - 40 = 0
x = -45 x = 40
hence roots are x = -45 and x = 40
we know that the speed of the train cannot be negative
hence,
x ≠ - 45
∴ the speed of the train is 40 km / hr