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x+ 1/x-2 = 2+ 1/x-1 2. The total area enclosed by lines y=|x| , |x|=1 and y=0 is 3. The minimum value of 3tan^2θ + 12cot^2θ is 4. If midpoint of join (x,y+1) and (x+1,y+2) is {3/2,5/2} then the midpoint of join of (x-1,y+1) and (x+1, y-1) is 5. If pand q are roots of equation x^2+px+q=0, then two values for p are 6.if the roots of x^2-ax+b=0 differ by unity then: a. B^2=1+4a b. a^2 =1+4b c. if x belongs to real no.s, a^2>4b d. a^2 +4b =1 7. Total no. of solutions of 2^x+3^x+4^x-5^x=0 is If a,b, c are three positive real numbers, then mnimum value of expression b+c/a + a+c/b + a+b/c is

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The above equation seems to have one real irrational root, and two imaginary roots. ======================== There are two triangles for the area given. O(0,0), (1,0) and (1,1) form one triangle. O(0,0), (-1,0), and (-1,1) form another triangle. Are a of both is same = 1/2. Total area = 1. ======================================

=========================== (x+x+1)/2=3/2 => x = 1 and (y+1+y+2)/2 = 5/2 => y = 1 mid point of (2,2) and (2, 0) is (2, 1) ==================================== as p is a root, substitute in place of x . p² +p*p + q = 0 => 2p² = - q q² + p q + q = 0 => 4p⁴ - 2 p³ -2p² = 0 , one possibility , p = 0, and q = 0. cancel 2 p² in above equation. 2 p² - p -1 = 0 p = [ 1 + - sqroot(1 +8) ] / 4 = 1 or -1/2 ================================ let roots be = s+1/2 and s - 1/2 sum of roots = a = 2s => s = a/2 product of roots = b = s² - 1/4 = (a²-1)/4 => a² = 1+4b ============ if x is real, then discriminant >= 0,, so a² - 4b >= 0 ======================