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1. Find all real numbers a that satisfy \frac{1}{64a^3 + 7} - 7 = 0.

 

2. Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.

 Apr 28, 2023
 #1
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1. A = -2

Expand out terms of the left hand side

1-7a³-49=-a³

-7a³-48=-a³

 

Taking out minus common from both sides and cancel them

-(7a³+48)=-(a³)

7a³+48=a³

 

Add -a³-48 on both sides

7a³+48-a³-48=a³-a³-48

6a³=-48

 

Divide both sides with 6

(6÷6)a³=(-48÷6)

a³=-8

 

Write -8 in the expansion form which is (-2)×(-2)×(-2)=-8

a³=(-2)³

 

From above it says that

a=-2

 

2. Sorry for this one I do not know. But I hope the answer up top will do something to satisfy you.

 Apr 28, 2023

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