Worksheet: Cubic Equations

In this worksheet, we will practice solving a cubic equation written as sum or difference of two cubes.

Q1:

Find the value of 𝑦 given that (2π‘¦βˆ’14)βˆ’36=28.

  • A βˆ’ 5
  • B9
  • C6
  • D18
  • E βˆ’ 8

Q2:

Given that π‘₯βˆˆβ„ and βˆ’π‘₯10=100π‘₯, determine the value of π‘₯.

Q3:

Determine the solution set of the equation 31βˆ’6π‘₯=βˆ’222π‘₯βˆ’698 in ℝ.

  • A  βˆ’ 5 5 6 
  • B  βˆ’ 4 3 
  • C  βˆ’ 3 2 
  • D  βˆ’ 2 3 
  • E  3 2 

Q4:

Solve the following equation 54π‘₯+1,814=βˆ’186, given that π‘₯ is in ℝ.

  • A  3 1 0 
  • B  βˆ’ 9 0 7 9 6 
  • C  9 3 9 0 4 
  • D  βˆ’ 3 1 0 
  • E  βˆ’ 1 0 3 

Q5:

Find the value of 𝑦 given that βˆ’1,000π‘¦βˆ’27=0.

  • A3
  • B βˆ’ 3 1 0
  • C 3 1 0
  • D βˆ’ 3

Q6:

Find the value of π‘₯ which satisfies the following equation βˆ’0.3π‘₯=48, given that π‘₯ is in β„šβ€².

  • A  ο„ž 1 1 6 0
  • B βˆ…
  • C βˆ’ √ 1 6 0 
  • D  √ 1 6 0
  • E βˆ’ ο„ž 1 1 6 0 

Q7:

Solve π‘₯+5=9.

  • A π‘₯ = √ 4 
  • B π‘₯ = √ 4 , π‘₯ = βˆ’ √ 4
  • C π‘₯ = √ 1 4 , π‘₯ = βˆ’ √ 1 4
  • D π‘₯ = √ 1 4 
  • E π‘₯ = √ 1 4  , π‘₯ = βˆ’ √ 1 4 

Q8:

If ο€Ήπ‘₯,π‘¦βˆ’4=ο€»βˆ’8,√4ο‡οŠ©, find the values of π‘₯ and 𝑦.

  • A π‘₯ = 2 , 𝑦 = 6
  • B π‘₯ = 4 , 𝑦 = 6
  • C π‘₯ = βˆ’ 2 , 𝑦 = 6
  • D π‘₯ = βˆ’ 6 , 𝑦 = βˆ’ 2

Q9:

Solve π‘₯=9.

  • A π‘₯ = 3
  • B π‘₯ = √ 3  , π‘₯ = βˆ’ √ 3 
  • C π‘₯ = √ 9  , π‘₯ = βˆ’ √ 9 
  • D π‘₯ = 3 , π‘₯ = βˆ’ 3
  • E π‘₯ = √ 9 

Q10:

Solve π‘₯=310.

  • A π‘₯ = ο„ž 3 1 0 , π‘₯ = βˆ’ ο„ž 3 1 0
  • B π‘₯ = ο„ž 3 1 0
  • C π‘₯ = ο„ž 3 1 0 
  • D π‘₯ = √ 3 1 0 , π‘₯ = βˆ’ √ 3 1 0
  • E π‘₯ = √ 3 1 0  , π‘₯ = βˆ’ √ 3 1 0 

Q11:

Find the solution set of π‘₯=7 in β„šβ€².

  • A  √ 7 
  • B  √ 7  
  • C  βˆ’ √ 7 , √ 7 
  • D  βˆ’ √ 7  

Q12:

If ο€Ήπ‘₯βˆ’7,π‘¦βˆ’6=ο€»1,||βˆšβˆ’64||ο‡οŠ©οŽ’, find (𝑦,π‘₯).

  • A ( 6 4 , 1 )
  • B ( βˆ’ 2 , 2 )
  • C ( 1 0 , 2 )
  • D ( 6 4 , 2 )

Q13:

Solve π‘₯=278.

  • A π‘₯ = 3 2
  • B π‘₯ = 3 8
  • C π‘₯ = 3 2 or π‘₯=βˆ’32
  • D π‘₯ = 3 8 or π‘₯=βˆ’38
  • E π‘₯ = 9 2

Q14:

Given that π‘₯8+7=1, find the value of π‘₯, and state whether it is a rational or irrational number.

  • A4, irrational
  • B 2 √ βˆ’ 6  , rational
  • C4, rational
  • D βˆ’ 4 8 , irrational
  • E 2 √ βˆ’ 6  , irrational

Q15:

If possible, find the value of π‘₯ which satisfies βˆ’0.216π‘₯=27, given that π‘₯ is in β„š.

  • A βˆ’ 2 0
  • B βˆ’ 5
  • CNo value exists.
  • D βˆ’ 9 5
  • E βˆ’ 1 5

Q16:

Determine the solution set of the equation βˆ’8π‘₯βˆ’12π‘₯+27βˆ’96π‘₯βˆ’216βˆ’27π‘₯+12π‘₯βˆ’π‘₯=βˆ’200οŠͺ.

  • A  1 5 , βˆ’ 1 5 
  • B { 5 , βˆ’ 5 }
  • C { 2 , βˆ’ 2 }
  • D  1 5 
  • E { 5 }

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