Решите неравенство _(sqrt(6-x))(6+x) + _(sqrt(6+x))(6-x) 5 .

Задача №17595: Неравенство

lo g_{6 - x} (6 + x) + lo g_{6 + x} (6 - x) ⩽ 5 ⟺ \frac{2 ln ( 6 + x )}{ln ( 6 - x )} + \frac{2 ln ( 6 - x )}{ln ( 6 + x )} ⩽ 5 ⟺ \frac{2 ln ^{2} ( 6 + x ) - 5 ln ( 6 + x ) ln ( 6 - x ) + 2 ln ^{2} ( 6 - x )}{ln ( 6 + x ) ln ( 6 - x )} ⩽ 0 ⟺ \frac{( ln ( ( 6 + x ) ^{2} ) - ln ( 6 - x ) ) ( ln ( 6 + x ) - ln ( ( 6 - x ) ^{2} ) )}{ln ( 6 + x ) ln ( 6 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( ( 6 + x ) ^{2} - ( 6 - x ) ) ( ( 6 + x ) - ( 6 - x ) ^{2} )}{( 5 + x ) ( 5 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( x ^{2} + 13 x + 30 ) ( - x ^{2} + 13 x - 30 )}{( 5 + x ) ( 5 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( x + 10 ) ( x + 3 ) ( x - 10 ) ( x - 3 )}{( x + 5 ) ( x - 5 )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 - 10 ⩽ x < - 5 - 3 ⩽ x ⩽ 3 5 < x ⩽ 10 ⟺ - 6 < x < - 5 - 3 ⩽ x ⩽ 3 5 < x < 6

lo g_{6 - x} (6 + x) + lo g_{6 + x} (6 - x) ⩽ 5 ⟺ \frac{2 ln ( 6 + x )}{ln ( 6 - x )} + \frac{2 ln ( 6 - x )}{ln ( 6 + x )} ⩽ 5 ⟺ \frac{2 ln ^{2} ( 6 + x ) - 5 ln ( 6 + x ) ln ( 6 - x ) + 2 ln ^{2} ( 6 - x )}{ln ( 6 + x ) ln ( 6 - x )} ⩽ 0 ⟺ \frac{( ln ( ( 6 + x ) ^{2} ) - ln ( 6 - x ) ) ( ln ( 6 + x ) - ln ( ( 6 - x ) ^{2} ) )}{ln ( 6 + x ) ln ( 6 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( ( 6 + x ) ^{2} - ( 6 - x ) ) ( ( 6 + x ) - ( 6 - x ) ^{2} )}{( 5 + x ) ( 5 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( x ^{2} + 13 x + 30 ) ( - x ^{2} + 13 x - 30 )}{( 5 + x ) ( 5 - x )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 \frac{( x + 10 ) ( x + 3 ) ( x - 10 ) ( x - 3 )}{( x + 5 ) ( x - 5 )} ⩽ 0 ⟺ ⎩ ⎨ ⎧ - 6 < x < 6 - 10 ⩽ x < - 5 - 3 ⩽ x ⩽ 3 5 < x ⩽ 10 ⟺ - 6 < x < - 5 - 3 ⩽ x ⩽ 3 5 < x < 6