I don't know how to solve...Can anyone help me??
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Answered by
10
Given expression is
Let's find the prime factorization of 2160.
So,
Prime factorization of 2160
can be rewritten as
So,
So, on comparing we get
Hence,
More Identities to know :-
(a + b)² = a² + 2ab + b²
(a - b)² = a² - 2ab + b²
a² - b² = (a + b)(a - b)
(a + b)² = (a - b)² + 4ab
(a - b)² = (a + b)² - 4ab
(a + b)² + (a - b)² = 2(a² + b²)
(a + b)³ = a³ + b³ + 3ab(a + b)
(a - b)³ = a³ - b³ - 3ab(a - b)
Answered by
22
Given :-
x³y²z = 2160
To Find :-
x² + y² + z²
Solution :-
x³y²z = 2160
Prime factorizing 2160
2 | 2160
2 | 1080
2 | 540
2 | 270
3 | 135
3 | 45
3 | 15
3 | 5
5 | 1
2160 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
2160 = 4¹ × 4¹ × 3³ × 5
2160 = 4⁽¹ ⁺ ¹⁾ × 3³ × 5
2160 = 4² × 3³ × 5
Now
x³y²z = 4² × 3³ × 5
x³ = 3³
x = 3
y² = 4²
y = 4
z = 5
Now
x² + y² + z²
(3)² + (4)² + (5)²
9 + 16 + 25
9 + 41
50
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