Question

if p+q+r=1 and pq+qr+pr=-1 and pqr=-1 find the value of p3+q3+p3​

Answer 1

Answer:

p3+q3+r3 = 1

Step-by-step explanation:

look at the third equation- pqr= -1

you cannot get the answer '1' unless all the no.s are 1

for eg- 1x1= 1 or -1x1= -1

2x1 $\neq$ 1

therefore: p, q, r= 1 or -1

since pqr= -1, one of the no.s have to be negative

as all the no.s are variables, any one of them can be negative

Let's assume:

p=1, q= -1, r=1:

now to verify, see if the assumption equates with all equations:

(p+q+r= 1) = (1 -1 +1= 1)

[pq+qr+pr= -1] = [(1 x -1)(-1 x 1)(1x1)= -1]

∴ p3+q3+p3= 1$^{3}$ + (-1$^{3}$) + 1$^{3}$= 1