स्पष्टीकरणासह प्रश्‍नसंच - समीकरणाची उकल - Maths & Resoning

1) ) 3x = 27

    Explanation: \[x = \frac{27}{3}\\ x = 9\]


    2) 3x + 7 = 22 तर x = ?

      Explanation: \[3x = 22 - 7\\ 3x = 15\\ x = \frac{15}{3}\\ x = 5\]


      3) \[\frac{5}{2}x + 3 = \frac{21}{2}\]

      Explanation: \[\frac{5x}{2} =\frac{ 21}{2} - 3\\ \frac{5x}{2} = \frac{15}{2}\\ 10x = 30\\ x = \frac{30}{10} = 3\]


      4) \[x^{2}+\frac{1}{x^2} = 79\] तर\[x^{}+\frac{1}{x} = ?\]

      Explanation: \[\frac{x+1}{x}^2 = 8\\ \frac{x+1}{x} = 9\]


      5) \[5) x+\frac{1}{x}= 4 तर x^{4} +\frac{1}{x^2}\]

        Explanation:\[x^{2} + \frac{1}{x^2 } = \left (\frac{x+1}{x} \right )^2 - 2 = 16 - 2 = 14\] त्‍याचप्रमाणे \[x^{4} + \frac{1}{x^4} = \left ( \frac{x^2+1}{x^2} \right )^2 - 2\\ 14^{2} - 2 = 194\]


        6) a + b = 10, a – b – 2 तर a2 + b2 = ?

          Explanation: a + b = 10
          a – b = 2


          2a = 12 a = 6 तर b = 4

          a2 + b2 = 62 + 42 = 52


          7) \[p - \frac{1}{p} = - 4\: तर \:p^{2} + \frac{1}{p^2} = ?\]

            Explanation: \[\left ( p-\frac{1}{p} \right )= -4\\ \left (p^2+\frac{1}{p^2} \right ) = \left ( p-\frac{1}{p} \right )^2 + 2\\ -4^{2} + 2 = 16 + 2 = 18\]


            8) a 2 – 3a – 1 = 0 तर a2 + 1 a 2 = ?

              Explanation:\[a^{2} - 3a - 1 = 0\\ a - 3 - \frac{1}{a} = 0\\ a - \frac{1}{a} = 3\\ \left (a^2+ \frac{1}{a^2} \right )= \left (a- \frac{ 1}{a} \right )^2 \times 2 \\= 3^{2} + 2 = 11\]


              9) a+b+c = 13 तर ab+bc+ca = 27 तर a 2+b 2+c 2 = 0

              Explanation:a+b+c=13, ab+bc+ca = 27


              a2+b2+c2 = (a+b+c) 2 -2(ab+bc+ca)

              = 13 2 – 2 x 27

              = 169 – 54 = 115