If a-1/(a-3)=5 then find the value (a-3)2+1/(a-3)2
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Answer:
value of a=7/2 and answer is 2
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Given:
a-1/(a-3)=5
To find:
If a-1/(a-3) = 5 then find the value (a-3)2+1/(a-3)2
Solution:
From given, we have,
a-1/(a-3)=5
a - 1 = 5(a - 3)
a - 1 = 5a - 15
15 -1 = 5a - a
14 = 4a
7 = 2a
∴ a = 7/2
Now consider,
(a-3)2+1/(a-3)2
= [(7/2) - 3]² + 1/ [(7/2) - 3]²
we get, 7/2 - 3 = [7 - (2 × 3)]/2 = (7 - 6)/2 = 1/2
∴ we have, (a - 3)² = 1/2
= (1/2)² + 1/ (1/2)²
= 1/4 + 1 / (1/4)
= 1/4 + 4
= [1 + (4 × 4)]/4
= [1 + 16]/4
= 17/4
∴ (a-3)2+1/(a-3)2 = 17/4
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