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Elza [17]
2 years ago
12

Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value

Mathematics
2 answers:
erik [133]2 years ago
7 0

\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70

\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70

\\ \tt\Rrightarrow y(2)(4)(7)=70

\\ \tt\Rrightarrow y(56)=70

\\ \tt\Rrightarrow y=\dfrac{70}{56}

\\ \tt\Rrightarrow y=\dfrac{5}{4}

#2

\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120

\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120

\\ \tt\Rrightarrow -y(2)(4)(7)=120

\\ \tt\Rrightarrow 56y=-120

\\ \tt\Rrightarrow y=\dfrac{-120}{56}

\\ \tt\Rrightarrow y=\dfrac{-15}{7}

Olegator [25]2 years ago
6 0

Answer:

  • i. y = 8, ii. y = -2

Step-by-step explanation:

  • (1 - y)(3 - y)(6 - y) = -70

We can see the divisors are 2 and 3 apart.

i.

<u>Factorize -70 so that divisors are 2 and 3 apart:</u>

  • - 70 = (- 2)*(- 5)*(- 7)

<u>The smallest one is 1 - y and -7:</u>

  • 1 - y = -7
  • y = 1 + 7
  • y = 8

ii

<u>Factorize 120 so that divisors are 2 and 3 apart:</u>

  • 120 = 3*5*8

<u>The smallest one is 1 - y and 3:</u>

  • 1 - y = 3
  • y = 1 - 3
  • y = -2
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