Let a complex number z ,   z ≠ 1 , satisfy log 1 2 z + 11 z - 1 2 ≤ 2 . Then, the largest value of z is equal to _________.

Question

Let a complex number z , &#160; z &#8800; 1 , satisfy log 1 2 z + 11 z - 1 2 &#8804; 2 . Then, the largest value of z is equal to _________.

Aicharya · Accepted Answer

log 1 2 z + 11 z - 1 2 &#8804; 2 &#8658; z + 11 z - 1 2 &#8805; 1 2 , &#8757; log a b &#8804; c &#8658; b &#8805; a c &#160; i f &#160; 0 &#60; a &#60; 1 &#8658; 2 z + 22 &#8805; z - 1 2 , &#8757; z &#8800; 1 &#160; &#38; &#160; z - 1 2 &#62; 0 &#8658; 2 z + 22 &#8805; z 2 + 1 - 2 z &#8658; z 2 - 4 z - 21 &#8804; 0 &#8658; z - 7 z + 3 &#8804; 0 &#8658; z &#8804; 7 &#8756; Largest value of z is 7

Let a complex number z ,   z ≠ 1 , satisfy log 1 2 z + 11 z - 1 2 ≤ 2 . Then, the largest…

Solution

Let a complex number z , &#160; z &#8800; 1 , satisfy log 1 2 z + 11 z - 1 2 &#8804; 2 . Then, the largest…

Solution

Let a complex number z , z ≠ 1 , satisfy log 1 2 z + 11 z - 1 2 ≤ 2 . Then, the largest…