Answer: a²+b² = -99/2
Step-by-step explanation:
Since we are given two equations, this equations will be solved simultaneously to get a² and b²
a³ - 3ab² = 47 ... 1
b³ - 3a² b = 52... 2
From 1, a(a² - 3b²) = 47...3
From 2, b(b² - 3a²) = 52... 4
Adding 3 and 4, we have;
a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)
a²+b²-(3b²+3a²) = 99
(a²+b²) -3(b²+a²)= 99
Taking the difference we have
- 2(a²+b²) = 99
a²+b² = -99/2
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The inverse of the equation y = x² - 4, x≤ 0 is 
<h3>How to determine the inverse of the equation?</h3>
The equation is given as:
y = x² - 4, x≤ 0
Swap the x and y values
x = y² - 4
Add 4 to both sides
y² = x + 4
Take the square root of both sides
Hence, the inverse of the equation y = x² - 4, x≤ 0 is
Read more about inverse equations at:
brainly.com/question/11302699
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