Question

Consider the forowing explanation for why 1=2
1. Start out Let y = x
2. Wply through by xxy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
Factor each side yxy) = (x+y-yl
5. Divide both sides by byly = x+y
6. Divide both sides by yyy=xy + yy
And so 1 = y + 1
8. Since x=y, xy = 11 - 1 - 1
& And so = 2
How is this possible?


Answer....​

Answer 1

Answer:

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Answer 2

Factorise the following expressions.

(i) a2 + 8a + 16

(ii) p2 − 10p + 25

(iii) 25m2 + 30m + 9

(iv) 49y2 + 84yz + 36z2

(v) 4x2 − 8x + 4

(vi) 121b2 − 88bc + 16c2

(vii) (l + m)2 − 4lm (Hint: Expand (l + m)2 first)

(viii) a4 + 2a2b2 + b4

ANSWER:

(i) a2 + 8a + 16 = (a)2 + 2 × a × 4 + (4)2

= (a + 4)2 [(x + y)2 = x2 + 2xy + y2]

(ii) p2 − 10p + 25 = (p)2 − 2 × p × 5 + (5)2

= (p − 5)2 [(a − b)2 = a2 − 2ab + b2]

(iii) 25m2 + 30m + 9 = (5m)2 + 2 × 5m × 3 + (3)2

= (5m + 3)2 [(a + b)2 = a2 + 2ab + b2]

(iv) 49y2 + 84yz + 36z2 = (7y)2 + 2 × (7y) × (6z) + (6z)2

= (7y + 6z)2 [(a + b)2 = a2 + 2ab + b2]

(v) 4x2 − 8x + 4 = (2x)2 − 2 (2x) (2) + (2)2

= (2x − 2)2 [(a − b)2 = a2 − 2ab + b2]

= [(2) (x − 1)]2 = 4(x − 1)2

(vi) 121b2 − 88bc + 16c2 = (11b)2 − 2 (11b) (4c) + (4c)2

= (11b − 4c)2 [(a − b)2 = a2 − 2ab + b2]

(vii) (l + m)2 − 4lm = l2 + 2lm + m2 − 4lm

= l2 − 2lm + m2

= (l − m)2 [(a − b)2 = a2 − 2ab + b2]

(viii) a4 + 2a2b2 + b4 = (a2)2 + 2 (a2) (b2) + (b2)2

= (a2 + b2)2 [(a + b)2 = a2 + 2ab + b2