Question

Please help w/Q.7 . :)

Answer 1

Step-by-step explanation:

• Given  
• Let x^2 – ab / 2x – a – b = p  
• So x^ - ab = 2xp – ap – bp = 0
• So x^2 – 2px – ab + ap + bp = 0
• So x^2 – (2p)x + (ap + bp – ab) = 0
• Now as x is real we have
• (- 2p)^2 – 4 (ap + bp – ab) > 0
•  4p^2 – 4 ap – 4bp + 4ab > 0
• So p^2 – ap – bp + ab > 0
•  (p – b) (p – a) > 0
• So t his will be possible when both terms are either positive or negative
• So (p – b)(p – a) is positive when p > b and p > a
• So (p – b) (p – a) is negative when p < b and p < a
• Therefore the given expression has no real value between a and b