Find x and y grade 10 math question .
Answers
Answer:
x = 196/9, y = 169/9 or x = 169/9, y = 196/9
Step-by-step explanation:
Let us assume √x = a and √y = b
⇒x = a² and y = b²
Now let us consider :
x√x + y√y =183
⇒a².a + b².b =183
⇒a³ + b³ =183 -----------equation(1)
Similarly y√x + x√y = 182 we can write as
⇒b².a+a².b=182
⇒ab(b+a)=182 -----------equation(2)
(a+b)³ = a³ + b³ + 3ab(a+b)
⇒(a+b)³ -3ab(a+b) = a³ + b³
⇒(a+b)³ -3*ab*182/ab = 183 (From equation 1 and Equation 2)
⇒(a+b)³- 546 =183
⇒(a+b)³ =729
⇒a+b= 3√729 ≈ 9.0
∴ a+ b =9 -----------------> Equation 3
Substitute the value in equation 2,
ab(a+b) = 182
=> 9ab = 182
=> ab = 182/9.
(a - b)² = (a+b)² - 4ab
=> 81 - 4*182/9 = (a-b)²
=> (a-b)² = 729 - 728/9
=> a - b = √1/9 = ±1/3 ------------------> Equation 4.
solve Equation 3 and Equation 4.
If a - b = 1/3 | If a - b = -1/3
a+ b =9 | a + b = 9
a - b = 1/3 | a - b = -1/3
------------------ | ------------------------
2a = 28/3 | 2a = 26/3
------------------- | -------------------
=> a = 14/3 | => a = 13/3.
2b = 26/3 | 2b = 28/3
=> b = 13/3 | b = 14/3
√x = 14/3, √y = 13/3 | √x = 13/3 , √y = 14/3
x = 196/9, y = 169/9 | x = 169/9, y = 196/9
Answer:
Value of x = 169/9
Value of y = 196/9