2023 Mathematics Competition

### Question 14

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### 10 comments

###### Rose James

1 year ago

2²^y +2^y+1-8=0

(2^y)²-2^y ×2¹-8=0

Let p =2^y

(P)²-(p×2) -8=0

P²-2p-8=0

P²-4p+2p-8=0

P(p-4)+2(p-4)=0

(P+2) (P-4) =0

P+2=0 or p-4=0

P=-2 or p=4

2^y =2²

Y=2

###### Victory Light

1 year ago

2^2y-8 = -2^y-1 clt

2^2y + 2^y-1 = 8

Apply law of indices remove same base

2y + y-1 = 8

3y-1 = 8

3y = 8+1

3y = 9

divide both side by 3

y = 3

###### Akinola Ajayi

1 year ago

Let 2^y =a

a²-8=-2a

a²+2a-8=0

Solving using quadratic formula

a=2 or -4

Recall a=2^y

Therefore y = 1

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