Question

how to do this sum. can anyone tell me fast

Answer 1

x²-1 = 0

x²=1

x=√1

x=1, x=-1

case 1 [x=1]

p[1]⁴+q[1]³+r[1]²+s[1]¹+u=0

p+q+r+s+u=0

p=-q-r-s-u............1

case 2  [x=-1]

p[-1]⁴+q[-1]³+r[-1]²+s[-1]¹+u=0

p-q+r-s+u=0

p+r+u=q+s.............2

sub 1 in 2

-q-r-s-u+r+u=q+s

2q+2s=0

2[q+s]=0

q+s = 0..................3

combaining 2 and 3

p+r+u=q+s=0

hence proved

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