This is the question please answer it fastly iwant the answer quickly. You have to find the values of a,b,c
Answers
Answer:
a=13,b=12,c=5 or a=5,b=4,c=-3
Step-by-step explanation:
Given---> a²-b²=c² ,a-b=1,c=a-8
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Solution---> a-b=1 => a-1=b
------------- a²-b²=c²
We have an identity p²-q²=(p+q)(p-q)
Applying above identity we have
(a+b)(a-b)=c²
putting b =a-1
=> (a+a-1){a-(a-1)}=c²
=> (2a-1) (a-a+1) =c²
=> (2a-1) (1) =c²
putting c=a-8 in it
=> 2a-1 = (a-8)²
we have an identity (x+y)²=x²+y²+2xy applying it
=> 2a-1=a²+(8)²-2(a)(8)
=> 2a-1=a²+64-16a
=> a²-16a-2a+64+1=0
=> a²-18a+65=0
Now we do factors by splitting the middle term we facotrize 65 in two factors whose sum is 18 these factors are 13 and 5 so
=> a²-(13+5)a+65=0
=> a²-13a-5a+65=0
=> a(a-13)-5(a-13)=0
=> (a-13)(a-5)=0
If a-13=0
a=13
Now b=a-1=13-1=12
Now c=a-8=13-8=5
If a-5=0
a=5
Now b=a-1=5-1=4
Now c=a-8=-3