Find the cube root of 9ab^2+(b^2+24a^2)√b^2-√3a^2
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Answers
Answer with explanation:
We have to find cube root of
To find the cube root of this expression,we will use the concept of complex number
Let,Z=x+ i y
Equating real and Imaginary part on both sides
Also,
So,
→ When , y=0, then , cube root of the expression is only real x, that is the expression itself, means,Z=x+i y=x,
Answer:
3a + √(b² - 3a²)
Step-by-step explanation:
9ab² + (b² + 24a²) (√(b² - 3a²))
Let say
√(b² - 3a²) = x
squaring both sides
b² - 3a² = x²
=> b² = x² + 3a²
Putting vales
9a(x² + 3a²) + (x² + 3a² + 24a²)x
= 9ax² + 27a³ + x³ + 27a²x
= 3(3a)x² + (3a)³ + x³ + 3(3a)²x
= (3a)³ + x³ + 3(3a)²x + 3(3a)x²
= (3a + x)³
= (3a + √(b² - 3a²) )³
9ab² + (b² + 24a²) (√(b² - 3a²)) = (3a + √(b² - 3a²) )³
Taking cube root both sides
=> [9ab² + (b² + 24a²) (√(b² - 3a²))]^(1/3) = 3a + √(b² - 3a²)
= 3a + √(b² - 3a²)