Question

4. The sum of squares of three consecutive positive numbers is 245.Find the largest number.

Answer 1

[HeY Mate]

Answer:

Let x = be the first number

Let x+1 = be the second number

Let x+2= be the third consecutive number

So,

x^2 + (x+1)^2 +(x+2)^2= 245

x^2 +[x^2+2x+1]+ [x^2+4x+4]= 245

=> Combining like terms

3X^2+ 6x+5 = 245

=> Subtracting 5 from both sides

3X^2+6x =240

=> Divide all terms by 3

x^2+2x = 80

=> Subtracting 80 from both sides

x^2+2x-80= 0

=> Factoring

(x+10)(x-8)= 0

x=-10 or x=8

So, the numbers could be 8,9,10 or -10,-9, -8 .

=> Verification

(64)+(81)+(100)= 245

I Hope It Helps You✌️