Question

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Answer 1

    9 ˣ ⁺ ² = 720 + 9 ˣ

We know,

   Aⁿ ⁺ ¹ = Aⁿ × A¹

Thus, Applying this in the given equation,

         9ˣ × 9² = 720 + 9ˣ

   ⇒   9ˣ × 81 = 720 + 9ˣ

  ⇒  9ˣ  × 81 - 9ˣ = 720

 ⇒ 9ˣ ( 81 - 1) = 720

 ⇒ 9ˣ  × 80 = 720

 ⇒  9ˣ = 720/80

 ⇒ 9ˣ = 9¹

On Comparing,

           x = 1

Answer 2

Answer:

ABCD is a quadrilateral and AC, and BD are the diagonals.

Sum of the two sides of a triangle is greater than the third side.

So, considering the triangle ABC, BCD, CAD and BAD, we get

AB + BC > AC

CD + AD > AC

AB + AD > BD

BC + CD > BD

Adding all the above equations,

2(AB + BC + CA + AD) > 2(AC + BD)

⇒ 2(AB + BC + CA + AD) > 2(AC + BD)

⇒ (AB + BC + CA + AD) > (AC + BD)

⇒ (AC + BD) < (AB + BC + CA + AD)

Step-by-step explanation: