Question

Pls solve the following equations -:
(a) 5x - 3 = -18
(b) 3y - 5 = y - 1
(c) 3p + 8 = 3 + p
(d) 9z + 8 = 4z - 7

Pls explain in steps.​

Answer 1

Step-by-step explanation:

f(x) = kx³ – 8x² + 5

Roots are α – β , α & α +β

Sum of roots = – (-8)/k

Sum of roots = α – β + α + α +β = 3α

= 3α = 8/k

= k = 8/3α

or we can solve as below

f(x) = (x – (α – β)(x – α)(x – (α +β))

= (x – α)(x² – x(α+β + α – β) + (α² – β²))

= (x – α)(x² – 2xα + (α² – β²))

= x³ – 2x²α + x(α² – β²) – αx² +2α²x – α³ + αβ²

= x³ – 3αx² + x(3α² – β²) + αβ² – α³

= kx³ – 3αkx² + xk(3α² – β²) + k(αβ² – α³)

comparing with

kx³ – 8x² + 5

k(3α² – β²) = 0 => 3α² = β²

k(αβ² – α³) = 5

=k(3α³ – α³) = 5

= k2α³ = 5

3αk = 8 => k = 8/3α

(8/3α)2α³ = 5

=> α² = 15/16

=> α = √15 / 4

Answer 2

a) 5x-3=-18

5x=-18+3

5x=-15

x=-15/5

x=-3

b) 3y-5=y-1

3y-y=-1+5

2y=4

y=4/2

y=2

c) 3p+8=3+p

3p-p=3-8

2p=-5

p=-5/2

d) 9z+8=4z-7

9z-4z=-7-8

5z=-15

z=-15/5

z=-3

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