Find the value of x if PQ = x^2 + 3, QR = 4 + 2x, and PR = 15 if Q is between P and R.

x=2

Step-by-step explanation:

PQ+QR=PR

=x^2+3+4+2x=15

=x^2+2x+7=15

=x^2+2x+7-15=0

=x^2+2x-8=0. (quadratic equation)

=(x+4)(x-2)=0. (factorise)

=x+4=0 or x-2=0

x=-4 or 2

we take x to be the positive value which is

x=2

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

the answer is here: : )

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