Advertisements
Advertisements
प्रश्न
If `bb((15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7)` then find the value of following ratio.
`[ b^3 - 2a^3]/[ b^3 + 2a^3]`
उत्तर
`(15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7`
Applying componendo and dividendo, we get
`[(15a^2 + 4b^2) + ( 15a^2 - 4b^2)]/[(15a^2 + 4b^2) - ( 15a^2 - 4b^2)] = [47 + 7]/[47-7]`
⇒ `[15a^2 + 4b^2 +15a^2 - 4b^2]/[15a^2 + 4b^2 - 15a^2 + 4b^2]` =`54/40`
⇒ `(30a^2)/(8b^2) = 27/20`
⇒ `a^2/b^2 = (27 xx 8)/( 20 xx 30) = 9/25`
⇒ `a/b = sqrt( 9/25) = 3/5`
` therefore [ b^3 - 2a^3]/[ b^3 + 2a^3]`
Divided by `b^3`
=`[ b^3/b^3 - (2a^3)/b^3]/[ b^3/b^3 + (2a^3)/b^3]`
= `[ 1 - 2 xx 27/125]/[1 + 2 xx 27/125]` ...`( a/b = 3/5 ⇒ a^3/b^3 = 27/125)`
= `[ (125 - 54)/125] /[(125 + 54)/125] `
=`71/179`
APPEARS IN
संबंधित प्रश्न
If `bb(a/b = 7/3)` then find the value of the following ratio.
`(5a + 3b)/( 5a - 3b)`
If `bb(a/b = 7/3)` then find the value of the following ratio.
`(2a^2 + 3b^2)/(2a^2 - 3b^2)`
If `bb(a/b = 7/3)` then find the value of the following ratio.
`(a^3 - b^3)/b^3`
If `bb((15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7)` then find the value of following ratio.
`a/b`
If `bb((15a^2 + 4b^2)/( 15a^2 - 4b^2) = 47/7)` then find the value of the following ratio.
`[ b^2 - 2a^2]/[ b^2 + 2a^2]`
5m - n = 3m + 4n then find the value of the following expression.
`["m"^2 + "n"^2]/["m"^2 - "n"^2]`
5m - n = 3m + 4n then find the value of the following expression.
`(3m + 4n)/(3m - 4n)`
If `bb(a/b = 2/3)` then find the value of the following expression.
`[ 4a + 3b ]/( 3b )`
If `bb(a/b = 2/3)` then find the value of the following expression.
`[5a^2 + 2b^2]/[ 5a^2 - 2b^2]`
If `bb("a"/"b" = 2/3)` then find the values of the following expression
`[a^3 + b^3]/b^3`
