Three consecutive natural numbers ae such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

The three consecutive natural numbers are 9,10,11

Step-by-step explanation:

Step 1 : -

Let x be the number

Given three consecutive natural numbers are x, x+1,x+2

Given data are three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

that is [tex](x+1)^2 = (x+2)^2 - x^2 +60{\tex]

step 2:-

on simplification on both sides are , we get

by using [tex](a+b)^2 = a^2+2 a b+b^2[\tex]

[tex]x^2+2 x+1 = x^2+4 x+4-x^2+60[\tex]

cancelling x^2 terms and simplify

[tex] x^2 -2 x-63=0[\tex]

now finding factors of [tex] 63 = 9 X 7[\tex]

[tex] x^2 - 9 x+7 x -63=0 [\tex]

[tex] x(x-9)+7(x-90 =0 [\tex]

[tex]( x+7)(x-9) =0 [\tex]

here x= -7 is not an natural number

so we have to take x=9

therefore the three consecutive natural numbers are

x,x+1,x+2

The three consecutive natural numbers are  9 , 10, 11

i get you, what you should do is think of the positive things that would come out of it. it will make yours parents proud and raise your grade. you should always try and if you can't focus tell the teacher.

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2