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प्रश्न
Show that :
`1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2] = 5`
उत्तर
L.H.S = `1/[ 3 - 2√2] - 1/[ 2√2 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2]`
= `1/[ 3 - √8 ] - 1/[ √8 - √7 ] + 1/[ √7 - √6 ] - 1/[ √6 - √5 ] + 1/[√5 - 2]`
= `1/[ 3 - √8 ] xx [ 3 + √8 ]/[ 3 + √8 ] - 1/[ √8 - √7 ] xx [ √8 + √7 ]/[ √8 + √7 ]+ 1/[ √7 - √6 ] xx [ √7 + √6 ]/[ √7 + √6 ] - 1/[ √6 - √5 ] xx [ √6 + √5 ]/[ √6 + √5 ] + 1/[√5 - 2] xx [ √5 + 2 ]/[ √5 + 2 ]`
= `[ 3 + √8 ]/[(3)^2 - (√8)^2] - [ √8 + √7 ]/[ (√8)^2 - (√7)^2 ] + [ √7 + √6 ]/[ (√7)^2 - (√6)^2 ] - [ √6 - √5 ]/[ (√6)^2 - (√5)^2] + [√5 - 2]/[ (√5)^2 - (2)^2 ]`
= `[ 3 + √8 ]/[ 9 - 8 ] - [√8 + √7]/[8 - 7] + [ √7 + √6 ]/[ 7 - 6 ] - [ √6 - √5 ]/[ 6 - 5 ] + [√5 - 2]/[ 5 - 4 ]`
= 3 + √8 - √8 - √7 + √7 + √6 - √6 - √5 + √5 + 2
= 3 + 2
= 5
= R.H.S.
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