if X + y = 7 and xy = 10 find 1 by Xcube + 1 by y cube
Answers
Solution :-
Given :-
- x + y = 7
- xy = 10
using :-
- (x - y)² = (x + y)² - 4xy
→ (x - y)² = (7)² - 4*10
→ (x - y)² = 49 - 40
→ (x - y)² = 9
→ (x - y) = 3
Adding ,
→ (x + y) + (x - y) = 7 + 3
→ 2x = 10
→ x = 5
Putting,
→ x + y = 7
→ y = 7 - 5
→ y = 2 .
Therefore,
→ 1/x³ + 1/y³
→ 1/5³ + 1/2³
→ 1/125 + 1/8
→ (8 + 125)/1000
→ (133/1000)
→ 0.133 (Ans.)
Answer:-
Given:
- x + y =7 ...........(1)
- xy = 10 ............(2)
Solution:-
Let’s focus on equation 1.
Now find the x from eq (1)
x = 7 - y
then substitute x=7-y in eq (2)
(7 - y)y = 10
7y - y² = 10
7y - y² - 10
-y² + 7y - 10
Quadratic Equation Formula;
(-b ±√(b²–4ac)) / (2a)
- a = -1
- b = 7
- c = -10
y= -7±√(7)²-4(-1)(-10)/2(-1)
y=-7±√49-40/-2
y=-7±√9/-2
y=-7±3/-2
y=-7-3/-2 and y=-7+3/-2
y=-10/-2 and y=-4/-2
y = 5
y = 2
Case : 1
y=5
x+y=7
x+5=7
x=7-5
x=2
Case : 2
y=2
x+y=7
x+2=7
x=7-2
x=5
Solutions: (2,5) (5,2)
case :1
Substitute x for 5 and y for 2
=1/(5)³+1/(2)³
=1/125+1/8
=125+8/1000
=133/1000
=0.133
case : 2
Substitute x for 2 and y for 5
=1/(2)³+1/(5)³
=1/8+1/125
=125+8/1000
=133/1000
=0.133