PlS aNsWeR tHiS qUeStIoN
Answers
Step-by-step explanation:
please make me as brainliest
Step-by-step explanation:
Given :-
T ={ x/ [(x+5)/(x-7) ]-5 = (4x-40)/(13-x) }
To find :-
Is T an empty set ? Justify your answer?
Solution :-
Given set :
T ={ x/ [(x+5)/(x-7) ]-5 = (4x-40)/(13-x) }
[(x+5)/(x-7) ]-5 = (4x-40)/(13-x)
=> [(x+5)-5(x-7)]/5 = (4x-40)/(13-x)
=> (x+5-5x+35)/5 = (4x-40)/(13-x)
=> (40-4x)/5 = (4x-40)/(13-x)
On applying cross multiplication then
=> (40-4x)(13-x) = 5(4x-40)
=> 520-52x-40x+4x^2 = 20x-200
=> 4x^2-92x+520 = 20x-200
=> 4x^2-92x+520-20x+200 = 0
=> 4x^2-112x+720 = 0
=>4(x^2-28x+180) = 0
=> x^2-28x+180 = 0
=> x^2-18x-10x+180 = 0
=> x(x-18)-10(x-18) = 0
=> (x-18)(x-10) = 0
=> x-18=0 or x-10 = 0
=> x = 18 or x= 10
x = 18 and 10
The set T = { x/x = 18 and 10 }
The set T has the element x is equal to 18 at the same time 10
=> So there is no value exist same time for x
=> So we can not write that type of elements in the set T.
So T is an empty set.
Answer:-
T is the empty set for the given problem
Used formulae:-
- A set having no elements in its is called an empty set or void set it null set.
- The cardinal number of an empty set is 0