Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value i. -70 ii. 120

2 answers
Question:

Find a value for y for which the expression (1-y)(3-y)(6-y) has each given value
i. -70
ii. 120

Answers

[tex]\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=-70[/tex][tex]\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=-70[/tex][tex]\\ \tt\Rrightarrow y(2)(4)(7)=70[/tex][tex]\\ \tt\Rrightarrow y(56)=70[/tex][tex]\\ \tt\Rrightarrow y=\dfrac{70}{56}[/tex][tex]\\ \tt\Rrightarrow y=\dfrac{5}{4}[/tex]#2[tex]\\ \tt\Rrightarrow (1-y)(3-y)(6-y)=120[/tex][tex]\\ \tt\Rrightarrow -y(1+1)(3+1)(6+1)=120[/tex][tex]\\ \tt\Rrightarrow -y(2)(4)(7)=120[/tex][tex]\\ \tt\Rrightarrow 56y=-120[/tex][tex]\\ \tt\Rrightarrow y=\dfrac{-120}{56}[/tex][tex]\\ \tt\Rrightarrow y=\dfrac{-15}{7}[/tex]

Answer:i. y = 8, ii. y = -2Step-by-step explanation:(1 - y)(3 - y)(6 - y) = -70We can see the divisors are 2 and 3 apart.i.Factorize -70 so that divisors are 2 and 3 apart:- 70 = (- 2)*(- 5)*(- 7)The smallest one is 1 - y and -7:1 - y = -7y = 1 + 7 y = 8iiFactorize 120 so that divisors are 2 and 3 apart:120 = 3*5*8The smallest one is 1 - y and 3:1 - y = 3y = 1 - 3y = -2

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