Thesolution set of the equation (2y-3)^{\frac{1}{3}}-(4y+5)^{\frac{1}{3}}=0ZS

ossidianaZ

ossidianaZ

Answered question

2021-09-16

The solution set of the equation (2y3)13(4y+5)13=0

Answer & Explanation

Sally Cresswell

Sally Cresswell

Skilled2021-09-17Added 91 answers

Step 1
Consider the provided equation,
(2y3)13(4y+5)13=0
Now, add (4y5)13 to the both sides,
(2y3)13(4y+5)13=0
(2t3)13(4y+5)13+(4y+5)13=(4y+5)13
(2y3)13=(4y+5)13
Take cube on both sides of the above equation,
(2y3)13=(4y+5)13
((2y3)13)3=((4y+5)13)3
2y3=4y+5
35=4y2y
Simplify the above equation,
35=4y2y
8=2y
y=4
Check:
Now, substitute the value of y=4 in the provided equation (2y3)13(4y+5)13=0
[2(4)3]13[4(4)+5]13?=0
(83)13(16+5)13?=0
(11)13(11)13?=0
0?=0
Which is true.
Hence, the solution set of the equation (2y3)13(4y+5)13=0 is {4}

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