SOLUTION: I am new to this subject and having difficulty in solving these problems. Please kindly help me. 1. Find three consequtive integers such that the sum of their squares is 77.3

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1. Find three consequtive integers such that the sum of their squares is 77.3
No solution. There are no three integers whose sum is 77.3
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2. solve equation w^3+5w^2-w=5
w^3+5W^2-w-5 = 0
The coefficients sum to zero so 1 is a root and (x-1) is a factor.
Use synthetic division to find the quadratic factor:
1)....1....5....-1....-5
........1....6.....5...|..0
Remainder = 0
Quotient = x^2+6x+5 which factors as (x+5)(x+1)
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(w-1)(w+1)(w+5)=0
w=1 or w=-1 or w=-5
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3. Factor completely z^4-81
= (z^4 - 3^4)
= (z^+9)(z^2-9)
= (z^2+9)(z+3)(z-3)
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Cheers,
Stan H.