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| 1. |
If A.M and G.M of two positive number a and b are 10 and 8 respectively find the number |
| Answer» {tex}let\\,two\\,numbers\\,be\\,a\\,and\\,b{/tex}{tex}A.M. = {{a + b} \\over 2} = 10{/tex}{tex}a + b = 20 \\ldots \\ldots \\left( 1 \\right){/tex}{tex}G.M. = \\sqrt {ab} = 8{/tex}{tex}ab = 64 \\ldots \\ldots \\left( 2 \\right){/tex}{tex}Now\\,{\\left( {a - b} \\right)^2} = {\\left( {a + b} \\right)^2} - 4ab{/tex}{tex} = {\\left( {20} \\right)^2} - 4 \\times 64{/tex}{tex} = 400 - 256{/tex}{tex}{\\left( {a - b} \\right)^2} = 144{/tex}{tex}a - b = \\pm 12 \\ldots \\ldots \\left( 3 \\right){/tex}{tex}solving\\,\\left( 1 \\right)\\,and\\,\\left( 3 \\right){/tex}{tex}a = 4,b = 16\\,or\\,a = 16,b = 4{/tex}{tex}hence\\,two\\,numbers\\,are\\,4\\,and\\,16\\,or\\,16\\,and\\,4.{/tex} | |