Step-by-step explanation:
Given that:
{(x²+y²)/(x²-y²)} = 17/8
On applying cross multiplication then
since, (a/b) = (c/d) ⇛a(d) = b(c)
Where, x = x²+y², b = x²-y², c = 17 and d = 8
So,
⇛17(x²-y²) = 8(x²+y²)
Multiply the number outside of the brackets with variables in the brackets on both LHS and RHS.
⇛17x²-17y² = 8x²+8y²
⇛17x²-17y² - 8x²-8y² = 0
⇛17x²- 8x² - 17y² - 8y² = 0
⇛9x² - 25y² = 0
⇛9x² = 25y²
⇛9/25 = y²/x²
⇛25/9 = x²/y²
⇛x/y = √(25/9)
⇛x/y = √{(5*5)/(3*3)}
⇛x/y = 5/3
Therefore, x:y = 5:3
Let x = 5a and y = 3a
Now, (x³+y³):(x³-y³)
= {(x³+y³)/(x³-y³)} = [{(x+y)(x²-xy+y²)}/{(x-y)(x²+x-y+y²)}]
= [{(5a)³ + (3a)³}/{(5a)³ - (3a)³}]
= [{(5*5*5*a*a*a) + (3*3*3*a*a*a)}/{(5*5*5*a*a*a) - (3*3*3*a*a*a)}]
= {(125a³ + 27a³)/(125a³ - 27a²)}
= {(152a³)/(98a³)}
= 152/98
Write the obtained fraction in lowest form by cancelling method.
= {(152÷2)/(98÷2)}
= 76/49
Therefore, , (x³+y³):(x³-y³) = 76/49
Answer: Hence, the required value of (x³+y³):(x³-y³) is 76/49.
Please let me know if you have any other questions.
