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Find the value of z such that 2(z-1)3 + 6(1-z)3 = 32?
- a)-2
- b)-1
- c)0
- d)1
- e)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the value of z such that 2(z-1)3 + 6(1-z)3 = 32?a)-2b)-1c)0d)1e)2...
⇒ 2(z-1)3 + 6(1-z)3 = 32
⇒ 2 [ z3 -1 - 3z(z-1) ] + 6 [1 - z3 - 3z(1-z)] = 32
⇒ 2 [ z3 - 1 -3z2 + 3z ] + 6 [ 1 - z3 -3z + 3z2 ] = 32
⇒ 2z3 - 2 - 6z2 + 6z + 6 - 6z3 -18z2 + 18z = 32
⇒ -4z3 + 12z2 - 12z + 4 = 32
Substract 32 from both sides we get,
⇒ -4z3 + 12z2 - 12z + 4 - 32 = 32 - 32
⇒ -4z3 + 12z2 - 12z - 28 = 0
⇒ -4( z + 1 )( z2 - 4z -7) = 0
⇒ ( z + 1 )( z2 - 4z -7) = 0
Then,
( z + 1 ) = 0
z = -1
or
( z2 - 4z -7) = 0
z = 2 + √3i, 2 - √3i
Most Upvoted Answer
Find the value of z such that 2(z-1)3 + 6(1-z)3 = 32?a)-2b)-1c)0d)1e)2...
Solution:
We are given the equation 2(z-1)^3 - 6(1-z)^3 = 32 and we need to find the value of z that satisfies this equation.
Simplifying the equation:
2(z-1)^3 - 6(1-z)^3 = 32
2(z-1)^3 - 6(-1)^3(z-1)^3 = 32
2(z-1)^3 + 6(z-1)^3 = 32
8(z-1)^3 = 32
(z-1)^3 = 4
z-1 = 2
z = 3
Therefore, the value of z that satisfies the equation is 3.
Answer: (e) 2
We are given the equation 2(z-1)^3 - 6(1-z)^3 = 32 and we need to find the value of z that satisfies this equation.
Simplifying the equation:
2(z-1)^3 - 6(1-z)^3 = 32
2(z-1)^3 - 6(-1)^3(z-1)^3 = 32
2(z-1)^3 + 6(z-1)^3 = 32
8(z-1)^3 = 32
(z-1)^3 = 4
z-1 = 2
z = 3
Therefore, the value of z that satisfies the equation is 3.
Answer: (e) 2
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