Question

Pleaze help me asap
And please no fake answers.

Answer 1

Explanation:

`\underline{ \underline{ \text{Given}}}` :

• a = dk³ , b = dk² , c = dk

`\underline{ \underline{ \text{To \: prove}}} :`

`\tt{ √(ab) - √(bc) - √(cd) = √((a - b - c)(b - c - d)) }`

`\underline{ \underline{ \text{Solution}}} :`

Left hand side ( L.H.S ) :

`\tt{ √(ab) - √(bc) - √(cd)}`

⟶
`\tt{ \sqrt{d {k}^(3) \cdot \: d {k}^(2) } - \sqrt{d {k}^(2) \cdot \: dk } - √(dk \cdot \: d) }`

⟶
`\tt{ \sqrt{ {d}^(2) {k}^(5) } - \sqrt{ {d}^(2) {k}^(3) } - \sqrt{ {d}^(2)k } }`

⟶
`\tt{ \sqrt{ {d}^(2) \cdot \: {k}^(2) \cdot \: {k}^(2) \cdot \: k } - \sqrt{ {d}^(2) \cdot \: {k}^(2) \cdot \: k \: } - \sqrt{ {d}^(2)k } }`

⟶
`\tt{ \sqrt{ {d}^(2) } \cdot \sqrt{ {k}^(2) } \cdot \: \sqrt{ {k}^(2) } \cdot \: √(k) } - \sqrt{ {d}^(2) }\cdot \: \sqrt{ {k}^(2)} \cdot \: √(k) \: - \sqrt{ {d}^(2) } \cdot \: √(k)`

⟶
`\tt{d {k}^(2) √(k) - dk √(k) - d √(k) }`

⟶
`\tt{ d√(k) \: ( {k}^(2) - k - 1) }`

Right Hand Side ( R.H.S) :

`\tt{ √((a - b - c)(b - c - d))}`

⟶
`\tt{ \sqrt{(d {k}^(3) - d {k}^(2) - dk)( d{k}^(2) - dk - d)} }`

⟶
`\tt{ \sqrt{ \{dk( {k}^(2) - k - 1) \} \: \{d( {k}^(2) - k - 1) \}} }`

⟶
`\tt{ \sqrt{ {d}^(2)k( {k}^(2) - k - 1) ^(2) } }`

⟶
`\tt{ \sqrt{ {d}^(2)k } \cdot \: \sqrt{ {( {k}^(2) - k - 1)}^(2) } }`

⟶
`\tt{ \sqrt{ {d}^(2) } \cdot \: √(k) \cdot \: \sqrt{( {k}^(2) - k - 1) ^(2) } }`

⟶
`\tt{d √(k) \: ( {k}^(2) - k - 1) }`

L.H.S = R.H.S

Hence , Proved !

Hope I helped ! ♡

Have a wonderful day / night ! ツ

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁