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The sum of the two consecutive odd number is 394. Find the numbers. |
| Answer» According to the question,the sum of the squares of two consecutive odd numbers is 394.Let the odd no. be 2x + 1{tex}\\therefore {/tex}\xa0Consecutive odd number = 2x + 1 + 2=2x + 3Now, according to question{tex}( 2 x + 1 ) ^ { 2 } + ( 2 x + 3 ) ^ { 2 } = 394{/tex}{tex}\\Rightarrow 4 x ^ { 2 } + 4 x + 1 + 4 x ^ { 2 } + 12 x + 9 = 394{/tex}{tex}\\Rightarrow \\quad 8 x ^ { 2 } + 16 x - 384 = 0{/tex}{tex}\\Rightarrow \\quad x ^ { 2 } + 2 x - 48 = 0{/tex}{tex}\\Rightarrow \\quad x ^ { 2 } + 8 x - 6 x - 48 = 0{/tex}{tex}\\Rightarrow {/tex}\xa0x(x + 8) - 6(x + 8) = 0{tex}\\Rightarrow(x-6)(x+8){/tex}{tex}\\Rightarrow x=6, x=-8{/tex}-8 get rejected, hence{tex}\\therefore {/tex}\xa01st\xa0number =\xa0{tex}2 \\times 6 + 1{/tex}= 13\xa0and second odd number = 15 | |