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Asked by mohit2pal | 03 May, 2019, 16:35: PM
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G i v e n colon space x comma y element of left square bracket 0 comma 10 right square bracket 3 to the power of s e c squared x minus 1 end exponent times square root of 9 y squared minus 6 y plus 2 end root less or equal than 1 rightwards double arrow 3 to the power of tan squared x end exponent times square root of 9 y squared minus 6 y plus 2 end root less or equal than 1 S i n c e comma space x element of left square bracket 0 comma 10 right square bracket comma space t h e space l e a s t space v a l u e space o f space x space i n space 0 rightwards double arrow T h e space l e a s t space v a l u e space o f space tan squared x space i s space 0 rightwards double arrow 3 to the power of tan squared x end exponent equals 3 to the power of 0 equals 1 rightwards double arrow 3 to the power of tan squared x end exponent greater or equal than 1 A l s o comma space 9 y squared minus 6 y plus 2 equals 9 y squared minus 6 y plus 1 plus 1 equals left parenthesis 3 y minus 1 right parenthesis squared plus 1 greater or equal than 1 space sin c e comma space left parenthesis 3 y minus 1 right parenthesis squared greater or equal than 0 T h e r e f o r e comma space 3 to the power of s e c squared x minus 1 end exponent times square root of 9 y squared minus 6 y plus 2 end root space c a n apostrophe t space b e space l e s s space t h a n space 1 T h e r e f o r e comma space space 3 to the power of s e c squared x minus 1 end exponent times square root of 9 y squared minus 6 y plus 2 end root equals 1 rightwards double arrow x equals 0 space a n d space square root of 9 y squared minus 6 y plus 2 end root equals 1 space i f space 3 y minus 1 equals 0 rightwards double arrow y equals 1 third H e n c e comma space open parentheses x comma y close parentheses equals open parentheses 0 comma 1 third close parentheses space i s space t h e space o n l y space s o l u t i o n space o f space t h e space i n e q u a l i t y space 3 to the power of s e c squared x minus 1 end exponent times square root of 9 y squared minus 6 y plus 2 end root less or equal than 1. H e n c e comma space t h e space n u m b e r space o f space s o l u t i o n s space i s space 1.
Answered by Renu Varma | 06 May, 2019, 13:51: PM

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