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.

  • Aβˆ’5
  • B9
  • C6
  • D18
  • Eβˆ’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.

  • Aο¬βˆ’556
  • Bο¬βˆ’43
  • Cο¬βˆ’32
  • Dο¬βˆ’23
  • E32

Q4:

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

  • A310
  • Bο¬βˆ’90796
  • C93904
  • Dο¬βˆ’310
  • Eο¬βˆ’103

Q5:

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

  • A3
  • Bβˆ’310
  • C310
  • Dβˆ’3

Q6:

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

  • AοŽ’ο„ž1160
  • Bβˆ…
  • Cβˆ’βˆš160
  • D√160
  • Eβˆ’ο„ž1160

Q7:

Solve π‘₯+5=9.

  • Aπ‘₯=√4
  • Bπ‘₯=√4, π‘₯=βˆ’βˆš4
  • Cπ‘₯=√14, π‘₯=βˆ’βˆš14
  • Dπ‘₯=√14
  • Eπ‘₯=√14, π‘₯=βˆ’βˆš14

Q8:

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

  • Aπ‘₯=2, 𝑦=6
  • Bπ‘₯=4, 𝑦=6
  • Cπ‘₯=βˆ’2, 𝑦=6
  • Dπ‘₯=βˆ’6, 𝑦=βˆ’2

Q9:

Solve π‘₯=9.

  • Aπ‘₯=3
  • Bπ‘₯=√3, π‘₯=βˆ’βˆš3
  • Cπ‘₯=√9, π‘₯=βˆ’βˆš9
  • Dπ‘₯=3, π‘₯=βˆ’3
  • Eπ‘₯=√9

Q10:

Solve π‘₯=310.

  • Aπ‘₯=ο„ž310, π‘₯=βˆ’ο„ž310
  • Bπ‘₯=ο„ž310
  • Cπ‘₯=ο„ž310
  • Dπ‘₯=√310, π‘₯=βˆ’βˆš310
  • Eπ‘₯=√310, π‘₯=βˆ’βˆš310

Q11:

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

  • A√7
  • B√7
  • Cο«βˆ’βˆš7,√7
  • Dο«βˆ’βˆš7

Q12:

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

  • A(64,1)
  • B(βˆ’2,2)
  • C(10,2)
  • D(64,2)

Q13:

Solve π‘₯=278.

  • Aπ‘₯=32
  • Bπ‘₯=38
  • Cπ‘₯=32 or π‘₯=βˆ’32
  • Dπ‘₯=38 or π‘₯=βˆ’38
  • Eπ‘₯=92

Q14:

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

  • A4, irrational
  • B2βˆšβˆ’6, rational
  • C4, rational
  • Dβˆ’48, irrational
  • E2βˆšβˆ’6, irrational

Q15:

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

Q16:

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

  • A15,βˆ’15
  • B{5,βˆ’5}
  • C{2,βˆ’2}
  • D15
  • E{5}

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