Maths questions(f.2)

1(a) Expand (a+1)^2
(a+1)^2
=a^2 + 2a + 1
b)(x+1+y)^2
=[(x+y)+1]^2
=(x+y)^2 + 2(x+y) +1
=x^2 +2xy +y^2 +2x +2y +1

2)1/a:1/b =2/3:5/7
b/a= 14/15
b= 14, a =15

3)
2a=5b
a/b=5/2
a:b=5:2

5b=4c
b/c=4/5
b:c=4:5

thus. a:b=5:2 and b/c=4:5
a:b:c=10:4:5

4)1/a:1/b=2:3
b/a=2/3
a:b=3:2
1/b:1/c=3:4
c/b=3/4
b:c= 4:3
thus, a:b= 3:2 and b:c = 4:3
a:b:c=6:4:3

1. (a) Expand (a+1)²

(a+1)²
= a² + 2(1)(a) + 1²
= a² + 2a + 1

(b) Hence, expand (x+1+y)² *[using result of (a)]

Let a = x+y

(x+1+y)²
= [(x+y)+1]²
= (a+1)² 【let a = (x+y)】
= a² + 2a + 1 【from the result of (a)】
= (x+y)² + 2(x+y) + 1
= x² + 2xy + y² + 2x + 2y + 1
= x² + y² + 2xy + 2x + 2y + 1

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Are you finding a:b?

2. 1/a:1/b =2/3:5/7

1/a : 1/b = 2/3 : 5/7

(1/a) / (1/b) = (2/3) / (5/7)

b/a = 2(7) / 3(5)

b/a = 14/15

a/b = 15/14

So a:b = 15:14

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3.If 2a=5b=4c, find a:b:c.

From 2a = 5b = 4c

we have
2a = 4c
a = 2c ......... (1)

we have
5b = 4c
b = 4c/5 .......... (2)

a :b :c
= 2c : 4c/5 : c 【from (1) and (2)】
= 2 : 4/5 : 1
= 10 : 4 : 5

So a:b:c = 10:4:5

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4.If 1/a:1/b:1/c=2:3:4, find a:b:c.

1/a:1/b:1/c = 2:3:4

we have
1/a : 1/c = 2:4
(1/a) / (1/c) = 2/4
c/a = 1/2
a/c = 2
a = 2c ........ (1)

we have
1/b : 1/c = 3:4
(1/b) / (1/c) = 3/4
c/b = 3/4
b/c = 4/3
b = 4c/3 .......... (2)

a:b:c
= 2c : 4c/3 : c 【from (1) and (2)】
= 2 : 4/3 : 1
= 6 : 4: 3

So a:b:c = 6:4:3