x = 7+4β3x = 7+4β3To find βx we proceed,x = 7+4β3To find βx we proceed,βx = β(7+4β3)x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofx = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β3x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β31/βx = 1/(2+β3)x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β31/βx = 1/(2+β3)Multiplying both numerator and denominator by 2 - β3, we getx = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β31/βx = 1/(2+β3)Multiplying both numerator and denominator by 2 - β3, we get1/βx = (2-β3)/(2-β3)(2+β3) = (2-β3)/(2Β²-β3Β²) =x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β31/βx = 1/(2+β3)Multiplying both numerator and denominator by 2 - β3, we get1/βx = (2-β3)/(2-β3)(2+β3) = (2-β3)/(2Β²-β3Β²) =1/βx = 2-β3x = 7+4β3To find βx we proceed,βx = β(7+4β3)βx = β(7+2x2β3)βx = β(7+2β3x4)βx = β(3+4+2β3x4)β¦.. {writing 7 = 3+4}If we observe RHS of βx we observe form ofβ(aΒ² + bΒ² +2ab) where a=β3 and b =β4Hence, βx =β(β3 +β4)Β² = β3 + β4 = 2+β3βx = 2+β31/βx = 1/(2+β3)Multiplying both numerator and denominator by 2 - β3, we get1/βx = (2-β3)/(2-β3)(2+β3) = (2-β3)/(2Β²-β3Β²) =1/βx = 2-β3Hence βx +1/βx = 2+β3 +2 -β3 = 4